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T H E 

PRACTICAL MINERS' 

OWN BOOK AND GUIDE, 

COMPRISING A SET OF 

TRIGONOMETRICAL TABLES, 

ADAPTED TO ALL PURPOSES OF MINING SURVEYING 5 


ALSO, A TREATISE ON THE ART AND PRACTICE OF 

^ssaging Silfrtr, Copper, f eafo nub Cm, 

WITH TABLES WHICH EXHIBIT AT ONE VIEW 
THE VALUE OF ASSAYED ORES. 


RULES FOR CALCULATING THE POWER OF STEAM AND 
WATER ENGINES; TOGETHER WITH A COLLEC¬ 
TION OF ESSENTIAL TABLES, RULES AND 
ILLUSTRATIONS EXCLUSIVELY 
APPLICABLE TO MINING 
BUSINESS. 


ALSO, SOME PLAIN ANp PRACTICAL 


REMARKS ON THE VENTILATION OF MINES, WITH SOME 
REMARKS UPON THE MIDDLE DIVISION OF EAST¬ 
ERN VIRGINIA COAL FIELDS. 


THE WHOLE INTRODUCED AND EXEMPLIFIED IN THE MOST PLAIN 
AND PRACTICAL MANNER. 


SIT JOB ATKINS, 3VT- E* 



J . W. RANDOLPH, 

No. 121 Main street, Richmond, Virginia, 
1860. 




ALTERED ACCORDING TO ACT OF CONGRESS, IN THE YEAR 1859, BY 

JOB ATKINS, 

IN THE CLERK’S OFFICE OF THE DISTRICT COURT OF THE UNITED STATES 1$ 
AND FOR THE EASTERN DISTRICT OF VIRGINIA, 


f (GIFT 
^ ESTATE OF 
\M14.UAM C. 
x APRI^* v:;A ' 






















* 

























































ES IR it f ^ * 


Page 31,—Table 1,—Example, see page 70. 
Page 31,—Table 1,—Example, see page 74. 
Page 31,—Teble 2,—Example, see page 79. 
Page 32,—Table 2,—Example, see page 82. 
Page 32,—Table 3,—Example, see page 84. 
Page 32,—Table 3,—Example, see page 85. 



















EXPLANATION OX THE DIAGRAMS 


TABT/E 1, PAGE 68. 

In this scheme the hypothenuse is made radius, consequently 
the other sides are the sine and co-sine of the included angle. 

Corollary. —Suppose one end of the line A B to remain 
at A while the other end B is moved round from e to f, then 
it is evident that the base C B will continue to increase, and 
the perpendicular B D to decrease, until the whole quadrant 
has been swept off. 

At 45°, or the middle of the quadrant, the base and per¬ 
pendicular are equal, and from that point to 90° the base will 
increase in the same ratio as the perpendicular decreased from 
1° to 45°, hence the propriety of the arrangement of this 
table in counting the degrees backward from 45 to 90. 

TABLE 2, PAGE 79. 

Here the perpendicular is made radius, therefore the hypoth¬ 
enuse A C will be the secant, and the base B C the tangent of 
the angle A. On this principle, it is clear that as the angle 
increases the base and hypothenuse will continue (throughout 
the whole quadrant) to increase in proportion. 

Table 3, page 83. 

In this diagrain the base is made radius, therefore by mathe¬ 
matical demonstration the perpendicular A C is the co-tangent 
and the hypothenuse B C the co-secant of the angle C and 
here it will be plain, that as the angle C is increased, the 
hypothenuse and perpendicular will proportionably be dimim 
ished. 


CONTENTS 


PART I . 

Page, 

Introduction ....,. 15 

Explanation and use of the tables..... 19 

Reduction of Decimals......... 23 

Addition u ........ 24 

Subtraction £< 24 

Multiplication “ ..,,,... 25 

Division “ 26 

Aliquot parts of a Fathom......... 26 

Preliminary Chapter......... 27 

Plane Trigonometry.32 

Diagonal Shafts................ 36 

Perpendicular Shafts... 37 

Diagonal Lodes. 47 

Perpendicular Shafts and Levels. 50 

Slides....,,...,,,. 55 

Horizontal Surveying...... 60 

Vertical “ 63 

Mensuration of Heights...,....... 63 

Miscellaneous Examples,,,,,,....,,. 65 

Table I.—Hypothenuse Radius..,,,........ 69 

Table II.—Perpendicular Radius... 76 

Table III.—Base Radius. 84 

Leveling. 86 

Horizontal or Traverse Surveying,.,,,,,. 89 



























CONTENTS. 


XV 

PART II. 

Page. 

Introduction .,,... 

Assay of Silver Ore... 101 

Assay of Copper Ore... 102 

Assay of Lead Ore....,,.,........ 

Assay of Tin Ore.,...,. 

Method of discovering the proportion of Silver contained in Copper 

Ore............. 

A Table showing the number of ounces, &c., of Silver contained in 

a ton of Ore, &c, &c.,. 

Silver Assay Table.......*. 108 

Power of Steam Engines,...,,,.,.,,....,.,...113 

Power of Water Engines... 

Table showing the square inches in a Cylinder.lit 

Table showing weight of Water in a Pump, &c.119 

Traverse Surveying..,,,...... 12° 

Table for converting Angles into Bearings.,,•«••••.131 

Plans and Seetions of Mines..,.,..150 

Underground Works and Ventilation.. 153 

Remarks upon the middle division of Eastern Virginia Coal Field 

and upon the use and value of Coal and Iron.164 

Searching for Coal,.,,.....,.....,.,....... 




















PREFACE. 


The subject upon which I have undertaken to write, stands 
pre-eminent in a commercial point of view, in respect to the 
national resources of this great country, and it is chiefly to the 
development of this portion of those resources that ] shall de¬ 
vote the following pages. At the same time, it may not be 
irrelevant that [ enter upon the important subject of the na¬ 
ture of coal and its geological position. According to Wer¬ 
ner, one of the most celebrated continental geologists, our 
Globe consists of successive deposits, amidst an ocean of wa¬ 
ter ; we have first, primitive rocks in a state of crystallization, 
and as the basis in which silica predominates, (i. e.) granite 
upon which all other formations rest; next to granite, we have 
slaty granite, then slates with a dimininished proportion of 
crystalline, serpentines, porphyries, all of which are less cry¬ 
stallized as they get farther from the granite. In the course 
of the changes which have taken place, he says, we find that 
primary deposits have been destroyed, and new rocks have 
been formed by the debris of the above mentioned primary 
formations. In these convulsions and at this era, living na¬ 
ture took date, and also coal, a mineral formed from vegeta¬ 
bles. The rents in the strata formed during these convul¬ 
sions became filled with rocks, such as granite, &c. forming 
faults or dykes. The metals have their ages and their epochs, 
of which copper is of the most recent formation; gold and iron 
have been formed in almost every gradation of this stupend- « 
ous process, and the nature of each specimen identifies the 
period of its formation. The coal beds are indiscriminately 
1 


A 



6 


PREFACE. 


accompanied by rocks and bands, which contain fossil impres¬ 
sions. It is worthy of remark that the carbonaceous sub¬ 
stances near to the surface, though they be identically the 
same kind of metals, are more rough and coarse in their com¬ 
position than those lower down, as they have not undergone 
the same compression. Reasoning from the general character 
of the coal formation, we can conceive the luxuriant vegeta¬ 
tion of that remote period to have been swept away by suc¬ 
cessive torrents into lakes and estuaries, and buried in succes¬ 
sion beneath deposits of mud and sand, which are now con¬ 
solidated into bands and rocks, whilst the vegetable matter 
has been converted by pressure and the operation of other 
agencies, into coal, which forms so important an ingredient 
in America’s national wealth. The minerals of this country, 
if properly developed and protected, would contribute more 
than any other description of property, to the wealth and ag¬ 
grandizement of the United States and to the well being of 
man. For whether we view them in regard to the employ¬ 
ment of capital and labor; the advancement of general com¬ 
merce ; the appropriation of the wonderful power of the 
steam engine; the support of the navy; or the development 
of the arts and sciences; they ought to .form the basis of the 
national wealth of America, and it is surprising to know that 
while France, England, Belgium and Prussia, so wisely hus¬ 
band and foster this description of property, the Americans 
have scarcely as yet ever turned their attention towards it in 
a legislative capacity, except it be to burthen it with taxation 
at home. The subject to which J have presumed to devote 
the following pages, is, I feel satisfied, of itself of sufficient im¬ 
portance to enlist the pen of some one more able to discuss it 
than I am; and I must therefore earnestly entreat the indulg¬ 
ence of the reader, whilst I acknowledge my inability to do 
sufficient justice to a subject of such vital importance. I will 
now beg leave to address a few words to Americans who have 
sons and those who act in the capacity of school masters in 
mining districts. 1 would ask the former, why they do not 


PREFACE. 


7 


have their sons instructed and taught the art of mining, and 
not be dependent upon foreigners as they now are to manage 
their mines. The occupation is not a degrading one, and 
while it is a dangerous one, the very thought of the good 
mankind derives from the use of coal and other minerals, 
ought to induce the young men of America to learn it. And 
why, I would enquire, should not the theory of the essential 
art of mining be taught in American schools and colleges, as 
well as it is in other countries, where colleges and schools of 
mines, are among the most noble establishments and contri¬ 
butes largely to the national prosperity and good. 

The science of Geology is still in its infancy, nor is the 
study of this comprehensive subject confined to philosophers. 
Nothing is more amusing to the practical miner than to read 
and hear the opinions of geologists. One grave Professor 
will tell us the lodes are secondary formations and have been 
subsequently filled from the surface. Another says, the ore 
or minerals have been thrown up into them by volcanic ac¬ 
tion ; and another, that it has been drawn into them sideways 
by electricity, having been held in solution in the adjoining 
rock. But I am sorry to say that but very few come to the 
right point and tell us that the whole is a contemporaneous 
creation: they will not do it, but will leave the truth .to be 
solved by unsophisticated men, while they are trying to re¬ 
concile impossibilities. As for the terms heave, slide, throw 
or anything else betokening subsequent disturbance, it is only 
a name and it matters not how ignorant some geologists may 
be of the fact, as the practical miner knows full well, that these 
phenomenas are the wise and admirable order of creation for 
the benefit of the human family. As to heaves or faults being 
secondary, the doctrine is fraught with absurdity and impos¬ 
sibility. We find down-throws and up-throws of several fa¬ 
thoms, and all the country and metals in its vicinity, without 
a single fracture and not the slightest sign that ever a hair’s 
breadth movement or agitation had taken place since the cre¬ 
ation of the world. If these secondary disturbances had taken 


8 


PREFACE. 


place, what a mighty wreck must have been felt and what a 
tremendous crash, if some supernatural power had caused this 
ponderous globe to shift some ten or twenty, and in many 
cases, eighty or a hundred fathoms, one part from another. 

Permit me to enquire how much benefit has mining ever 
received from all the geologists or their lectures. I know 
not a single instance in all the explorations that J have 
seen or heard of, that any good or assistance has emanated 
from their theoretical exertions, worth a straw. They have, 
most of them, rejected the inspired history of the creation of 
the world, and their doctrine is most of it replete with error, 
inconsistency and contradiction. Why do they not base their 
foundation on the sublime account so minutely given us in 
the Scriptures and then follow nature in all her grand and 
stupendous subterranean operations, and then they would 
discover a world of harmonious wonder, and would bring to 
light, to the admiration and benefit of the human family, the 
cause and effect of the magnificent order of every part of 
creation that is allowed to fall under the inspection of man¬ 
kind. It is not a little surprising that the statistics of the 
American coal fields should be so little known in this 
country, and more especially by those that own the land con¬ 
taining coal and other minerals in the State of Virginia. This 
surprise is increased when we consider how convenient it is 
to railroads and tide water, and its quality, and how replete it 
is with interesting facts to the owners of it, to the geologist 
and to the practical miner. If geologists would obtain more 
practical information from working miners, they would soon 
learn better than to make war against the mechanism of nature’s 
laws as some of them now do. But it is not so much to be 
wondered at, as history informs us that the great Sir Isaac 
Newton supposed at one time that the moon was straying 
from its path by slow degrees, insomuch, that its accumulation 
of error, after long ages, would break up the equipoises of our 
system, and that it would require an outstretching of the 
Almighty’s arm to set it back in its right place again, as we 


PREFACE. 


9 


mortals rectify the errors of a house clock by moving the 
hands. But La Grange, a French astronomer, after revising 
the computations of Newton, found, what will always be found 
when man dares to question the workmanship of his Maker, 
that the error was not in the celestial machinery but in the 
earthly observer. And so it is with minerals and every thing 
else. Every thing has been done in a manner to suit the 
necessities of mankind, though it may appear strange to 
us. No part of the natural world seems to grow old. The 
sun is not shorn of its brightness; the lightning lags not with 
decrepitude; time writes no wrinkles on the azure brow of 
the great ocean—the briny flood distills as fresh water as ever, 
and when this water has risen from the sea on the wings of 
evaporation, the winds diffuse it over the earth, the cold 
condenses it into drops, and gravitation brings it down to the 
surface, where it nourishes all kinds of vegetation and sustains 
all life, and then passes into the briny ocean again. The 
sentinels and multitudinous host of agencies which the great 
Ruler of the Universe has stationed at every point of His 
domain, never sleep at their posts, and never fail to execute 
their exact duty in obedience to His unchangeable laws. Age 
never dims their sight, nor slackens their speed, nor weakens 
their force, nor abates their fidelity. The material universe is 
not matter alone, it is filled with scientific treasures incon¬ 
ceivable and boundless; but practical knowledge obtained the 
keys to the apartments containing these precious treasures 
which are within the reach of every American citizen. 

J hope my readers will pardon me for occupying so much 
more of their time than I intended to, in the preface of this 
work, and hope it will not be uninteresting. I would like to 
say more on the subject of the earth and its relations, for I 
believe, that at some future day, chemistry will beautify the 
earth equally as much as astronomy has glorified the Heavens. 
And I believe, that as great a wonder as the birth of the 
telegraphic communication from city to city was, and the con¬ 
struction of the locomotive, that the intellectual genius of the 


10 


PREFACE. 


white man will, at no very distant period, invent substitutes 
in their places, as superior to them as they are to their pre¬ 
decessors. As the publication of this work has been delayed 
from pecuniary reasons till after Virginia soil and Southern 
institutions have been invaded by a set of robbers and mur¬ 
derers of the deepest dye, I shall make a few remarks in this 
work which would not have been embraced in it had it not 
taken place. It appears that nearly all over the Southern 
States the people are forming Southern rights associations, and 
withdrawing their patronage from the Northern States, in 
order to bring Northern fanatics and those that continue their 
anti-American acts, to their senses, which is just and right, all 
reasonable men will admit, but it is amazingly surprising that 
the South are so blind to their own interest as to desire to 
lavish their custom and patronage on a great deal worse and 
more powerful enemy than ever the North was or ever will 
be. England can say to Northern Abolitionists, “ I am the 
root and ye are the branches; my sheep hear my voice and 
follow me.” If it had not been for English interference, on 
the subject of slavery, the agitation upon it would have ceased 
long ago. Look at the language used only a few months ago 
by one Hamilton Hill, Secretary of Oberlin College—he wrote 
to England, soliciting funds to aid him, and other anti-Ameri¬ 
can traitors like him, in preventing the execution of justice 
against English aliens for robbing American citizens by forcing 
slaves to leave their masters against their wishes. He ex¬ 
presses himself as follows : He says, “Although I have been 
secretary of an American College for nearly twenty years, 
neither that or anything else ever has or ever can destroy my 
devotion to my native country, England.” Look at the 
language of those powerful enemies against Southern in¬ 
stitutions. That great agitator, George Thompson. Lord 
Brougham, and thousands as powerful as him. Dr. Mac- 
Kay, who has written a work on America, abuses Southern 
institutions in the most unlimited terms. He says, “The 
Southern railroads are badly constructed, and the farms 


PREFACE. 


11 


on Southern plantations are a desolation in consequence of 
slave labor, &c., &c.” If the South desire to do herself good, 
she should weaken the fortifications of her foes by not 
patronizing them, in the way of trade, and strengthen her own 
fortifications by encouraging and protecting all kinds of 
Southern trade within her own borders, and especially the 
iron manufactories and the coal mining operation; if she will 
do this, she will have an emigration from France, England, 
Ireland and Scotland and Germany, composed of scientific 
men, who will not only make new inventions, but will come 
and invest their capital on Southern soil and develop her re¬ 
sources, which are immeasureable in extent and incomputable 
in value. 


ILLUSTRATION OF THE CHARACTERS. 


-j- plus or more, the sign of addition, signifying that the 
numbers or quantities between which it is placed are to be 
added together. 

— minus or less, the sign of subtraction, denoting that the 
lesser of the two quantities between which it is placed is to 
be taken from the greater. 

X into, the sign of multiplication, signifying that the quan¬ 
tities between which it is placed are to be multiplied together. 

-r- by, the sign of division; signifying that the former of 
the two quantities between which it is placed is to be divided 
by the latter. 

: as or to, :: so is, the sign of an equality of ratios, denot¬ 
ing that the quantities between which they are placed are 
proportional to each other. Thus, 2 : 3 :: 4 : 6, denotes that 
2 is to 3 as 4 is to 6. 

= equal to, the sign of equality; signifying that the quan¬ 
tities between which it is placed are equal to each other. Thus 
6 + 4 =10, shows that 6 added to 4 is equal to 10. 

Angle. 

° Degrees. 

7 Minutes. 

A given line is represented by a stroke or dash, ( I ) as the 
base A B in the triangle on page 33, and a required line by a 
cipher ( o) as in the legs of the same triangle. 




ABBREVIATIONS. 


Deg. Degrees. 

Min. Minutes. 

Fath. Fathoms. 

Ft. Feet. 

In. Inches. 

Hyp. Ilypothenuse. 
Perp. Perpendicular. 
Comp. Complement. 
Tab. Tabular. 

Dec. Decimal. 

N. North. 

S. South. 


E. East. 

W. West. 

Prob. Problem. 

Ex. Example. 

Ansr. Answer. 

Dia. Diagram. 

Cwt. Hundred weight. 
Qr. Quarter. 

Lbs. Pounds. 

Oz. Ounces. 

Dwt. Pennyweight. 
Grs. Grains. 


1 
































































































































































THE 


PRACTICAL MINERS’ GUIDE. 


INTRODUCTION. 

It is an acknowledged fact, that subterraneous surveying in 
all its varieties, is one of the most difficult and momentous 
part of the duty of practical Mine agents : to assist them in 
that important operation, is the chief design in giving publicity 
to these tables. Notwithstanding the great improvements, 
which of late years have been made in the art of surveying, 
the most intelligent miners universally admit that the prac¬ 
tice is still very imperfect; nay, so far are they from any de¬ 
terminate and general system, that two persons can scarcely 
be found who adopt the same method, consequently some 
plain scheme founded on pure mathematical principles, is a 
great mining desideratum. Aware of the opposition which is 
so apt to arise against all attempts at innovation of an old and 
established habit, which however faulty in itself, custom may 
have stamped with an imaginary perfection, it may be necessary 
to make a few observations in support of this work, and endeav¬ 
or to prove its advantages over most of the preceding modes 
of performing a surveying operation in every respect. Not a 
great many years ago, the customary way of ascertaining the 
perpendicular and horizontal lines corresponding with a 
diagonal shaft, was by the very uncertain, expensive and tardy 



16 


INTRODUCTION. 


practice of dropping a plumb line from the back to the bottom, 
there fixing a roller or platform, and repeating the process 
from the brace to the foot of the shaft. This usage is largely 
explained in u Pryce’s Treatise on Mines and Mining,” (a cele¬ 
brated English work, published by subscription about the 
year 1776,) and therein described as the only system then 
known. 

It is true this most objectionable measure is now exploded, 
but not without great reluctance by many of its old practition¬ 
ers, and it was a long time before they could be prevailed on to 
abandon it, notwithstanding its glaring inconveniences accom¬ 
panied with the loss of time and waste of property. By 
inserting this defectiveness in our predecessors, we have no 
other design than to caution managers of mines in Ameri¬ 
ca, to guard against the too prevalent propensity of rejecting 
any new system merely because it is new, or its utility not 
discerned at first sight, and to induce them to give the subject 
an impartial investigation before they pass a conclusive judg¬ 
ment thereon. 

The use of mathematical instruments is now partially known 
i- the mining world, and certainly those agents who are well 
acquainted therewith, possess a decided advantage over others 
who are not; for doubtless, this science has the pre-eminence 
in a high degree over every other method heretofore employed 
in surveying. But without intending to undervalue instru¬ 
mental operation, we appeal to the experience of our scien¬ 
tific readers for support, in avouching that the process is ever 
liable to errors of considerable extent, and which are prone to 
slide in unaccountably ; but it is a palpable fact, that in point¬ 
ing or sweeping off the angles, an almost imperceptible de¬ 
viation will create a serious departure from truth ; and even 
in the course of bisecting, trisecting, inscribing, describing, 
and circumscribing; also, in drawing parallels, raising or de- 
mitting perpendiculars, the operation, even with the greatest 
care, is exposed to considerable mistakes, and so sensible are 
all professional men of this defect, that instrumental opera- 


INTRODUCTION. 


tioii is never resorted to, or relied on, in any case where great 
accuracy is required. 

But when we reflect on the laborious duties of the practical 
mine agent, and how much these duties are calculated to dis¬ 
qualify him in performing a geometrical plan with that deli¬ 
cacy and precision which the operation so indispensably 
demands, we then become established in my opinion, of the 
necessity of a work of this kind, and of its superiority over 
every other system hitherto introduced in subterranean 
surveying. 

Should any be yet disposed to advocate the existing prac¬ 
tice, and to contend that it is fully adequate to the desired 
purpose, we beg permission to enquire of such person, why 
it is that mistakes so commonly occur in sinking shafts and 
driving levels in most of our mines. That irreparable errors 
do frequently happen, is a truth too notorious for contradic¬ 
tion or dispute, and sometimes even under the superinten¬ 
dence of men whose knowledge, circumspection and experi¬ 
ence, no one presumes to call in question; consequently a 
more convincing proof than this cannot be adduced, of the 
fallibility of the best modern practice, and the necessity for 
the introduction of a more perfect system. Should it be 
inquired wherein the merit of this work is considered to 
consist, we answer, first, accuracy, and it will be discovered 
at a glance that every operation of the principle tables is 
wrought out to give places of decimals, or the ten thousandth 
part of an inch, consequently we may affirm without fear of 
confutation that in this property we outvie every other system. 
Secondly, plainness. Of this quality, our expert readers will 
be convinced at first sight, and will need no instruction for 
enabling them to apply the numbers readily, and we do not 
hesitate to say, that by the help of the rules and examples a 
common school boy will find no insurmountable difficulty in 
solving most abstruse problems relevant to surveying. Thirdly, 
despatch. To this desirable property no other system has an 
equal claim, or can, with any chance of success, enter into 


18 


INTRODUCTION. 


competition with our method, inasmuch as an answer in most 
cases may be obtained by the tables in less time than is neces¬ 
sary to make a preparation for performing the operation in 
any other way. 

And now having briefly endeavored to set forth the work 
in a true light, we commit it to the judgment of a liberal and 
discerning people, and should it be instrumental in happily 
preventing the grievous errors which are so prevalent in mining 
operations, and which we are bold to say, must in the nature 
of things continue to take place by the old practice; or should 
it only help to relieve the minds of faithful superintendents 
from that painful anxiety and suspense which never fails to 
harass them during the progress of any considerable work, 
whereby a heavy responsibility rests on them for the accuracy 
of their surveying, or should it in any other way, have the 
happy tendency of promoting the interest of mining, we shall 
not regret the labor, pain, expense, privation, trouble and 
perplexity it has cost us, even though we should never receive 
any other compensation. 


EXPLANATION AND USE OF THE TABLES. 


After so many preliminary observations, it will be necessary 
to say but little under this head, having already anticipated 
several things by way of introduction, which properly belong 
here. The reader will observe that the work is composed of 
three distinct tables, for the obvious reason of making each 
side of the triangle radius; and'certainly without such an 
arrangement it would have been incomplete. In each case the 
radius, or given side is one fathom, being the most convenient 
and familiar proportion that could have been introduced. The 
principal calculations, every quarter, or fifteen minutes of a 
degree, and extend from 1 to 89 degrees, being sufficiently 
extensive and minute for mining purposes (the angle of any 
intermediate division not being distinguished or required;) 
and here it must be observed, that the divisions are expressed 
by 15, 30 and 45 minutes, which numbers represent J, and 
f of a degree. The first and most essential table is that 
wherein the hypothenuse, or longest side is made radius, ex¬ 
tending- nearly throughout the quadrant, and every calculation 
wrought out to five decimal places of an inch, hereby giving 
a direct answer in exact ratio to six feet of the given side, to 
the ten thousandth part of an inch. Perhaps there may be a 
little difficulty at first, with persons unacquainted with mathe¬ 
matical order, in reading the first table. It must be remarked 
that from 1° to 45, or the middle of the quadrant, the degrees 
and parts are all on the left hand side descending the base 
stands in the adjoining columns, and the perpendicular on the 
same line to the right, but beyond that point the degrees will 
be found on the right hand side ascending, and then it must 
be specially noted that the perpendicular and base will have 



20 


THE PRACTICAL MINERS’ 


changed their positions, tiie base now standing on the right 
hand, and the perpendicular on the left hand side. Jn the 
second table the perpendicular is given, and the angles extend 
to 60°. One valuable mining property of this is, that it gives 
at sight the underlay in a fathom of every angle within the 
range of 60°, including the division; so that if it is required 
to know the underlay in a fathom on any degree, or quarter 
of a degree between 1 and 60, it will be immediately discov¬ 
ered by an inspection of the base in the column adjoining the 
given angle in this table. In the third and last table, the base 
is given and as the application of this part of the work is not so 
general as the preceding, the angles have been given in degrees 
only; nevertheless this table is indispensable on some occa¬ 
sions, especially in leveling or driving adits. It will be found 
like the second table, to extend from 1 to 60 degrees. 

Having thus briefly stated the nature of the work under 
each separate head, it only remains for us, after a few general 
observations, to recommend the learner to the inspection of 
the following examples, for we believe that one practical opera¬ 
tion will do more towards giving him a clear understanding 
or comprehension of the subject, than a volume written ex¬ 
pressly thereon, confined to mere speculative description. It 
may be remarked that in almost every instance the geometri¬ 
cal construction of the figure is introduced with the calcula¬ 
tion, which will tend to the satisfaction of the practitioner, 
and improvement of those young men who may have a desire 
to engage in this noble occupation. In conclusion we would 
remark, that the same attention must be paid in taking the 
angle, and measuring the given line when these tables are 
used, as if the operation was formed any other way. It is a 
common practice in mining, to take the angle of underlaying 
shafts with the cover of the compass and a plumb line; and 
in short drafts with great care, this method may answer well 
enough; but when any very important work is to be performed 
we would strongly recommend the application of a more 
perfect instrument for ascertaining the angles, for it is well 


OWN BOOK AND GUIDE. 


21 


known that if this part of the process should not be correct, 
the result of the whole work must be erroneous as a matter 
of course; and indeed it is next to impossible to distinguish 
the minutia of an angle with any tolerable degree of certainty 
by the foregoing method. There doubtless are instruments 
much better adapted to the work, both for speed and accura¬ 
cy, than the common compass, and it is a matter of surprise 
that they have not been more generally introduced in our 
mines. Of these instruments the Theodolite certainly stands 
unrivalled for taking both horizontal and vertical angles. It 
is not our design to enter into controversy on this subject, 
those who imagine the sextant or quadrant graduated on the 
cover of the compass well calculated for the purpose, let them 
continue to use it, only we would especially note, that should 
an error ensue, it ought by all means to be attributed to the 
real cause, and to that only, for as in all trigonometrical ques¬ 
tions, the angle and side are always given to find the other 
parts of the triangle, consequently the sum of the one, and 
length of the other are pre-supposed to have been correctly 
ascertained previous to the commencement of any other 
operation. Finally, for the learner’s sake, we observe that^s 
the tables exhibit only the relative proportions to the radius 
of one fathom or six feet, and are wrought out to five places 
of decimals to an inch, it becomes necessary that every one 
who would use this work successfully should have some 
knowledge of decimated arithmetic, because he will have in 
most cases to multiply for the whole numbers, and take parts 
for the fraction of the fathom. For example, suppose the given 
side to be the hypothenuse, measuring 16 fathoms, 3 feet and 6 
inches, he will then have to take out the numbers opposite the 
given angle in the tables, and multiply them by 16, for the base 
and perpendicular respectively, then divide half of the tabu¬ 
lar measure for the three feet, and one-sixth of the remainder 
for the six inches, and add them together for the sum of the 
required sides of the tri-angle. We have therefore introduced 
the following rules and examples in decimals, which are sufii- 


22 


THE PRACTICAL MINERS’ 


cient to enable any one hitherto unacquainted with this branch 
of aiithmetic, to use the tables with the greatest facility, 
and I would here remark for the encouragement of the 
beginner, that is, if he does not understand the system we 
advocate in this work, not to be discouraged, but to go on 
as the author has done, and combine practice with theory, 
and it will all appear in a short time, as clear as the mid¬ 
day sun. 


HYP 

100 . 

Links. 

HYP. 

100 . 

Links. 

HYP. 

100 . 

Links. 

^ of elev. 
or depres. 

Deduct 
fr. each 
100 Iks. 

of elev. 
or depres. 

Deduct 
fr. each 
100 Iks. 

£ of elev. 
or depres. 

Deduct 
fr. each 
100 Iks 

40 

I 08' 

£ 

19° 

57' 

6 

35° 

54' 

19 

5 

44 

h 

21 

34 

7 

36 

52 

20 

7 

01 


23 

04 

8 

37 

49 

21 

8 

7 

1 

24 

30 

9 

38 

35 

22 

9 

57 


25 

50 

10 

39 

39 

23 

11 

29 

2 

27 

08 

11 

40 

32 

24 

12 

50 

2 * 

28 

22 

12 

41 

25 

25 

14 

04 

3 

29 

32 

13 

42 

16 

26 

15 

12 

3i 

30 

41 

14 

43 

07 

27 

16 

16 

4 

31 

47 

15 

43 

57 

28 

17 

15 

4J 

32 

52 

16 

44 

46 

29 

18 

12 

5 

33 

54 

17 

45 

34 

30 

19 

06 

5i 

34 1 

55 

18 ,j 



I did not intend when I commenced writing this work, to 
embrace the above table in it, but hope it will not be objected 
to by my readers, inasmuch as I am induced to believe that it 
will be useful in mining surveying. 







































OWN BOOK AND GUIDE. 


23 


REDUCTION OF DECIMALS. 

Rule. —Multiply the decimal by the number of parts in the 
next less denomination, and cut off as many places to the 
right hand as there are places in the given decimals. 

EXAMPLE. 

What is the value of .75014 of a fathom ? 

6 

4.50084 

12 

6.01008 


ft. in. 

Ans. 4 6.01008. 

What is the value of .93862 of a yard ? 

3 


2.81586 

12 


9.79032 


ft. in. 

Ans. 2 9.79032. 

What is the value of .27734 of a foot ? 

12 


3.32808 


Ans. 3.32808. 

fath. ft. in. , . . 

Reduce 5 4 6.32 to feet, inches and decimals. 

6 

- in. 

Ans. 34 6.32. 










24 


THE PRACTICAL MINERS’ 


ADDITION OF DECIMALS. 

Rule.— Place the numbers so that the decimal points may 
stand directly under each other, add up as in simple addition. 

EXAMPLE. 

What is the sum of 3.72 and 14.7368 and 146.2 and .728 
and 5.034 ? 

Q 79 

14.7368 

146.2 

.728 

5.034 


170.4188 


ft ' in ' a in - 

What is the sum of 2 11.9942 and 1 4 09658? 
1 4.09658 


4 4.09078 


Add together the following measures, viz : 

fath. ft. in. dec. 

6 4 2.260 

0 1 11.47298 

19 0 3.087 

64 5 9.9746 

0 0 2.70643 


91 0 5.50101 


SUBTRACTION OF DECIMALS. 

Rule.— Arrange and cut off the decimals as in addition. 
example. 

fath. ft. in v 

From 4 2 9.7824 
Take 2 4 8.91773 


1 4 0.86467 










OWN BOOK AND GUIDE. 


25 


MULTIPLICATION OF DECIMALS. 

Rule.— Multiply as in whole numbers, and cut off as many 
figures from the product as there are decimals in the multi¬ 
plier and multiplicand. 

EXAMPLE. 


fath. 

ft. 

in. 

Multiply 2 

4 

7.92486 bv 24. 

6 

16 

3 

11.54916 



4 6x4—24 

66 

3 

10.19664 


Multiply 


fath. ft. in. 


9 3 1.4872 by 37. 

6 


57 

0 

8.9232 



6 

342 

4 

5.5392 

9 

3 

1.4872 

352 

1 

7.0264 


Here we multiply by 6 
twice because 6 times 6 
are 36, and add the given 
number which makes it 
equal to 37, or 6X64 - !” 
37. 


ft. in. 

Multiply 14 9.746 by 12 

12 


177 8.952 












26 


THE PRACTICAL MINERS’ 

DIVISION OF DECIMALS. 

Rule. —Divide as in whole numbers, and cut off as many 
figures in the quotient as the decimal places in the dividend 
exceed those of the divisor. 

EXAMPLE, 

fath. ft. in. 

Divide 2 4 3.7 by 6 



6)2 

4 

3.7 




0 

2 

8.61 



fath. ft. 

7)4 2 

in. 

10.30994 


fath. 

8)15 

ft. 

5 

0.3316 

0 3 

10.04427 


1 

5 

10.5414 


ALIQUOT PARTS OF A FATHOM TABLE. 


PARTS. 


FEET 

INCHES. 

i 

Of a fathom is 

3 

0 

i 

ditto 

2 

0 

i 

ditto 

1 

6 


ditto 

1 

0 

i 

ditto 

0 

9 

i 

ditto 

0 

8 

tV 

ditto 

0 

6 

tV 

ditto 

0 

4i 

tV 

ditto 

0 

4 


ditto 

0 

3 


REMARKS. 

It has been observed that the radius in every case is 6 feet 
or 1 fathom, consequently the number of fathoms in the given 
side, whether that side be hypothenuse, perpendicular or base, 
will be the multiplier of the tabular numbers^ and should 
there be a fraction in the multiplier, the multiplicand must be 
divided by that fraction agreeably with the rule of practice. 





















OWN BOOK AND GUIDE. 


27 


The table of aliquot parts of a fathom in the adjoining, will be 
found useful in facilitating this part of the process. In some 
of the following examples, the product has been obtained in 
fathoms and parts, but we would recommend the learner to 
carry on the work in feet, (except in cases where the answer 
is required in fathoms,) as he will find it more simple and ex¬ 
peditious, we speak of the multiplicand or number multiplied, 
the multiplier must invariably be fathoms, and should the 
given side be denominated in feet, it must be divided by 6, to 
bring it into fathoms, before the operation is begun by the 
foregoing cases. It may be lurther noticed that when any of 
the given sides in the tables amount to 6 feet, they are ex¬ 
pressed in fathoms, &c., but whenever it may be required to 
produce the answer in feet, &c., the numbers should be re¬ 
duced to that measure before they are multiplied, and this can 
be done by mere inspection, viz: 


fath. ft. 

Table 2d, ( Base, 1 1 

/^52° ( Hyp. 1 3 


in. ft- * n * 

8.1560 > (Base, 7 8.1560 
9.6053 5 state t Hyp. 9 9.6053 


PRELIMINARY CHAPTER 

TO THE 

PRACTICAL SURVEYING EXAMPLE. 


It must have been matter of regret to every reflecting, well 
informed and interested person, that (previous to the present 
work,) nothing has ever been published, with a design to 
assist the American miner in his subterraneous operation, and 
while the press has teemed with publications, distinctly and 
exclusively adapted to benefit the navigator, the architect, the 
sculptor, the surveyor and the mechanic and artisan, not a 
single effort has ever been made to extricate the miner from 




28 


THE PRACTICAL MINERS’ 


the disadvantage under which he has ever labored, (solely for 
the want of a plain, concise, practical and scientific treatise on 
subterraneous surveying, accompanied with appropriate tables,) 
although his profession yields to none in importance and 
utility, in fact, it may be said, in a certain sense, to be the 
parent of every art and science in the world—the use of me¬ 
tallic substances, in some shape or other, being indispensable 
in every one of them—nevertheless, this highly essential art 
has hitherto been totally disregarded by all classes of mathe¬ 
maticians, and while the famous invention of logarithms has 
caused the science of trigonometry to soar to the very skies, 
and traverse old ocean’s vast and unfathomable expanse—the 
unsupported miner has been left to struggle under the greatest 
disadvantage, with nearly as little obligation to geometrical 
science, as his antediluvian progenitors, and although he has 
done everything that deep thought, strong, natural understand¬ 
ing, unwearied perseverance and inventive genius, (unassisted 
by tiigonometrical demonstration,) could possibly accomplish; 
yet, for the want of mathematical light, his exertions have 
been ineffectual and insufficient to disentangle him from the 
difficulties with which he has been encircled; hence, his 
avocation has, in general, been replete with toil, anxiety, 
apprehension, disatisfaction and disappointment. 

How far the present work is adapted to answer the great 
end in contemplation, must be left for the judgment of the 
mining world to decide; and we doubt not but the defects, (real 
or imaginary,) which may be considered to exist in the appli¬ 
cation, will be passed over and excused by every liberal 
minded man on the grounds already stated in the'preface; 
having an unshaken confidence that the fundamental principles 
of the work comprised in the trigonometrical tables, will be 
found plain, true and unexceptional. 


OWN BOOK AND GUIDE. 


29 


DEFINITION OF RIGHT-ANGLED TRIANGLES. 

In order to mse the following tables with due effect, there 
is no necessity that the reader should understand anything of 
the science of trigonometry, that part of the work having 
been accomplished already to his hand, so that, by the help 
of a few of the common rules of arithmetic, he may obtain 
with the greatest ease and certainty, everything required to 
be known in the geometrical part of mining. Previous to an 
elucidation of the simple method of working by tables, it may 
be satisfactory to introduce the operation by a few preliminary 
observations and extracts on the nature and properties of 
right-angled triangles. Plane trigonometry is the art of 
measuring the sides and angles of triangles described on a 
plane surface, or of such triangles as are composed of straight 
lines. 

The theory of triangles is the very foundation of all geo¬ 
metrical knowledge, for all straight-lined figures may be 
reduced to triangles. The angles of a triangle determine only 
its relative species and are measured in degrees, minutes and 
seconds, but the sides determine its absolute magnitude, and 
may be expressed in fathoms, yards, feet or any other lineal 
measure. 

THEOREMS. 

A right angle triangle (the only kind generally necessary to 
be treated of for mining purposes,) is that which has one right 
angle in it, the longest side or that opposite to the right angle, 
is called the hypothenuse, the other two, are called the legs 
or sides, or the base and perpendicular; or by Euclid’s defi¬ 
nition, in a right angle triangle, the side opposite to the right 
angle, is called the hypothenuse, and of the other sides, that 
upon which the figure is supposed to stand, is called the base, 
and the remaining side, the perpendicular. The three angles 
of every triangle are together equal to two right angles, or 
180° The greater side of every triangle has the greater angle 
2 


30 


THE PRACTICAL MINERS’ 


opposite to it. The squares of two sides of a triangle are to¬ 
gether double of the square of half the base, and of the square 
of a straight line drawn from the vertex to Jbisect the base. 
The sum of the three angles of every plane triangle being 
equal to half a circle, or 180°, it therefore follows that if 
either acute angle in such triangle be taken from 90°, the 
remainder will be the other acute angle, or the complement.— 
The supplement of any angle is what that angle wants of 180°, 
hence the supplement of any one angle is always equal to the 
sum of the other two. 

A few other properties of right-angled triangles may be 
worthy of notice, viz: when the angle opposite the base is 
30°, the hypothenuse is exactly double the length of the base. 
When the angles are 45°, the base and perpendicular are equal. 
When the angle opposite the base is 60°, the hypothenuse is 
double the length of the perpendicular. 

Application.— To show how a knowledge of the forego¬ 
ing theorems may be rendered useful in mining practices, sup¬ 
pose in the triangle, ABC, on page 33, the base AB, repre¬ 
sented a drift or cross cut, and the side AC, a lode, making an 
angle with the base of 66° 30', consequently the angle A must 
be 23° 30', because it requires that number of degrees to con¬ 
stitute a right angle, the complement of the angle A, or 180°, 
the supplement of the triangle ABC; again, suppose the angle 
C of the diagonal shaft CA, page 34, was found to be 39° 
30', then the opposite angle A must contain 50° 30'; we now 
approach towards the actual use of the tables, and have suc¬ 
ceeded, we hope, in clearing all impediments out of the learn¬ 
ers way, so that he will find no difficulty in readily applying 
the numbers to surveying operations. We have previously 
set a few examples of the mere act of taking out the primes, 
and have studiously endeavored to render everything as per¬ 
spicuous and comprehensible as the nature of the work would 
possibly admit. But should any one have gone thus far and 
still find an obscurity hanging over him, so that he can not pen¬ 
etrate into the nature of the subject as he would wish, or as 


OWN BOOK AND GUIDE. 


31 


he may have expected, yet let him not be discouraged, this 
will always be the case with every one who calculates on ful¬ 
ly comprehending anything connected with mathematics by 
definition or description only. Let him steadily, attentively, 
and perseveringly proceed with the examples, and if he is 
properly interested in the matter, he will soon find the 
subject open with plainness to his mind, and convey to him 
the incontrovertible assurance of the truth of the calcula¬ 
tions, as well as the correctness of his own views, ideas, or 
conceptions of the subject. 

TABLE 1.— Example. 

When the angle is 9° and the hypothenuse 1 fathom, what 
is the length of the other two sides of the triangle respec¬ 
tively ? 

in. ft. in. 

Ans. Base, 11.26328, perp. 5 11.11356. 

EXAMPLE. 

When the angle is 48° 15', or 48|°,* and the hypothenuse 
1 fathom, what are the length of the other sides ? 


ft. in. ft. in. 

Ans. Base, 4 5.71613, perp. 3 11.94348. 

TABLE II.— Example. 

When the angle is 35° 45', or 35§°, and the perpendicular 
1 fathom, what is the length of the hypothenuse and base re¬ 
spectively ? 

ft. in. fath. ft. in. 

Ans. Base, 4 3.8326, hyp. 1 1 4.7165. 


*In this example, as the angle exceeds 45°, it will be found standing 
on the right hand side of the page, (as already explained,) and the de¬ 
nomination of the required sides will be found at the bottom. A little 
attention to this order will prevent the mistake, which may otherwise 
take place by an inversion of the base and perpendicular. 




32 


THE PRACTICAL MINERS’ 


EXAMPLE. 

Given the angle 59° 30', perpendicular 1 fathom, the other 
sides are required ? 

fath. ft. in. fath. ft. in. 

Ans. Base, 1 4 2.23] 7, hyp. 1 5 9.8612. 

TABLE III.— Example. 

Given the angle 5°, base 1 fathom, the hypothenuse and 
perpendicular are required ? 


fath. ft. in. fath. ft. in. 

Ans. Hyp. 11 2 10.10734, perp. 11 2 6.96374.' 

EXAMPLE. 

Given the angle 30°, base 1 fathom, the other sides are re¬ 
quired? 

fath. ft. in. fath. ft. in. 

Ans. Hyp. 2 0 0, perp. 1 4 4.70766. 


PLANE TRIGONOMETRY 

BY THE TABLES. 


CASE I. 


When the hypothenuse is given. 

Rule. Look in the first table, and against the given angle 
stands the base and perpendicular, answering to one fathom 
of the hypothenuse, take out these numbers and multiply 
them, respectively, by the length of the hypothenuse. 


NOTE.-The foregoing examples serve only to exemplify the man- 
ner of taking out the primes from the tables, and as the given side is 
exactly 1 fathom, of course the tables give a direct answer. In the fol¬ 
lowing examples, the mode of taking out the tabular numbers is pre- 
cisely as the foregoing, but the number of fathoms contained in the 
length of the given side, will be the multiplier of the other sides of the 

O * *3 






OWN BOOK AND GUIDE. 


33 


EXAMPLE. 

Given the angle 23° 30', and the hypothenuse 12 fathoms, 
the base and perpendicular are required ? 

OPERATION. 

Base. Perpendicular. 

Feet 2. 4.70993 Feet 5. 6.02833 

12 12 

28. 8.51916 66. 0.33996 


BY CONSTRUCTION. 


Process. 


Scale—40 feet to an inch. : 


Draw the line A B of any length, make 
the angle C=23° 30' by a scale of chords 
or with a protractor draw the hypothenuse 
A C=72 feet from a scale of equal parts. 
From C let fall the perpendicular C B, 
then A B C is the triangle required. A B, 
measured by the same scale of equal parts, 
will be 28 feet 8^ inches, and B C will 
be 66 feet. 


A 



When the perpendicular is given. 

Rule. —Look in the second table, and opposite the given 
angle will be found the base and hypothenuse corresponding 
to one fathom of the perpendicular; multiply these numbers 
separately by the length of the perpendicular. 

EXAMPLE. 

Given the angle 39° 30' and perpendicular 9 fathoms 3 feet; 
the hypothenuse and base are required ? 








34 


THE PRACTICAL MINERS’ 


OPERATION. 


fath. 

ft. 

in. 


fatli. 

ft. 

in. 

3U| 0 

4 

11.3522 

3 | i | 

1 

1 

9.3096 

1 1 


9 



9 

7 

2 

6.1698 


11 

3 

11.7864 

0 

2 

5.6761 


0 

3 

10.6558 

Base.—7 

4 

11.8459* 

Hyp.— 

•12 

1 

10.4412 


BY CONSTRUCTION. 


Process. 

Draw the line A B of a 
sufficient length, at any point B 
erect the perpendicular B C, 
which make equal to 57 feet 
by a scale of equal parts. At 
C make the angle=39° 30 / the 
complement of A. From C 
draw the hypothenuse and it 
will cut the base A B in the 
point A, then will A B measure 
47 feet, and A C 73 feet 10 inches. 

CASE III. 

When the base is given. 

Rule. Look in the third table, and opposite the given 
angle, (as in former cases,) the corresponding numbers to one 
fathom of the base will be seen, which being multiplied by 
the given length of the base, produces the hypothenuse and 
perpendicular. 


* K has been before observed that it would be better to brim? the 
answer out in feet than in fathoms as in the last case. 


C 














OWN BOOK AND GUIDE. 


35 


EXAMPLE. 


Given the angle 20 degrees, and base 28 feet 9 inches, the 
hypothenuse and perpendicular are required ? 


ft. 


£ 20 ° 


i 

17 

6.51392* 

i 


4 



70 

2.05568 


* 

8 

9.25696 

i 

£ 

2 

11.08565 

i 

2 

2.31424 



Hyp.—84 0.71253 


ft. 

16 

in. 

5.81837* 

4 

65 

11.27348 

8 

2.90918 

2 

8.96972 

2 

0.72729 

■78 

11.87967 


BY CONSTRUCTION. 


Process. 

Draw the base A B which make= 
28 feet 9 inches, from a scale of equal 
parts, at B erect the perpendicular B C, 
make the angle A=70° and draw the 
hypothenuse A C to cut the perpendicu¬ 
lar B C in the point C, then will A C 
measure 84 feet, and B C 78 feet 11^ 
inches. 


V 



* These numbers stand in the tables in fathoms, &c., the hypothenuse 
will be found 2 fathoms, 5 feet 6 inches, 8tc., and the perpendicular 2 
fathoms, 4 feet 5 inches, &c. 















36 


THE PRACTICAL MINERS' 


APPLICATION OF THE TABLES 

TO 

DIAGONAL SHAFTS. 


REMARKS. 

As in the foregoing cases each side of the triangle is dis¬ 
tinctly made radius, it follows that every problem in oblique 
surveying, &c., can be solved by one or the other of these 
cases, because,, in every instance, a side and the angles are 
already given. 

GENERAL RULE. 

When the hypothenuse is given, work by case the first. 

When the perpendicular is given, work by case the second. 

When the base is given, work by case the third. 

EXAMPLE I. 

A diagonal shaft A B was found to measure 84 feet,* and 
the angle of declination observed to be 48 degrees, required 
the base B C, and perpendicular A C. 


by case i. 



Whe " the given line is denominated in feet, it must be brought into 
fathoms by dividing it by 6, (the number of feet in a fathom,) thus in 
the above example, the shaft being 84 feet, is 14 fathoms, and, there¬ 
fore, the numbers are multiplied by 7 and 2, which are equal to 14. 















OWN BOOK AND GUIDE. 


37 


EXAMPLE 2. 

A perpendicular shaft BC, measuring 57 feet, was found to 
intersect an underlaying shaft, AC, whose angle of acclivity 
was observed to be 50° 3CU, required the length of the under¬ 
laying shaft AC, and the distance from the perpendicular at 
the surface AB ? 



by case ii. 


/50° 30' 
comp. 
39° 30' 


ft. in. 

ft. in. 

;) ||| 4 11.3522 

Hyp. | | | 7 93.096 

< Base I I 9 

1 1 ^ 

44 6.1698 

69 11.7864 

2 5.6761 

3 10.6548 

AB 46 11.8459 

AC 73 10.4412 


Note.— In the above example, the angle having again been taken 
with the horizon, the operative angle will be 39° 30', because 50° 30' 
gQO_ 39 o 3 Q/ > We may also observe that the length of the shaft being 
57 feet, the multiplier is 9| or 9 fathoms, 3 feet. 










38 


TIIE PRACTICAL MINERS’ 


EXAMPLE 3. 

A horizontal cross-cut BC, from the foot of a diagonal BA, 
to a perpendicular shaft CA, was found to measure 224 feet, 
8 inches, and the angle of acclivity (taken at B, the foot of 
the shaft) 40 degrees, I require the respective lengths of .the 
hypothenuse AB, and perpendicular AC ? 

A 



Z40° 

Comp. 

50° 


ft. in. 

7 9.98932 # 

12 


A B 


93 

11.87184 

3 

281 

11.61552 

7 

9.98932 

2 

7.32977 

0 

10.44325 

293 

3.37786 


ft. 

in. 


5 

0.41517 



12 


60 

4.98204 



3 


181 

294612 


5 

0.41517 


1 

8.13839 


0 

6.71279 

188 

6.21247 


o oqqqo • ' r 1& JlumDer ^ands m the table 1 fath. 1 ft 

9 98932 in, and the angle having been taken at the foot of the shaft 
the complement of that angle (i. what wants of 90 o) mustte 
used, therefore, the above tabular numbers will be found in the column 
opposite 50 , being the complement of 40°. 
























OWN BOOK AND GUIDE. 


39 


EXAMPLE 4. 

When a lode has changed its underlay. 

Rule. —Take out the numbers opposite the given angles, 
and work them by the former cases, then add their sums 
together, respectively, for the answer. 

In surveying a shaft sunk on a lode, it was found that the 
first draft B D measured 71 feet on an angle of 14° 45', but 



from that depth to the foot of the shaft C the angle proved to 
be 40° 15', and the length D C 54 feet, required the distance 
from the brace of the diagonal B, where a perpendicular shaft 
ought to be sunk, in order to come down exactly at the foot 
of the underlay; also the depth of the perpendicular AC? 











40 


the practical miners' 


Z14° 4 5 ' 


OPERATION. 


Base, 
fath. ft. in. 


O 1 6.33 J 34 
12 


3 0 3.97608 
0 0 3.05522 


3 0 0.92086 


Base. 

. . fath. ft. in. 

Z40° 15'=0 3 10.52093 
9 


5 4 10.68837 


Summary of Bases, 
fath. ft. in. 

3 0 0.92086 

5 4 10.68837 


8 4 11.60923 
6 


Perpendicular. 

fath. ft. in. 

0 5 9.6273 
12 


11 3 7.5276 
0 0 11.6045 


11 2 7.9231 


Perpendicular. 

fath. ft. in. 

o 4 6.95274 
9 


6 5 2.57466 


Sum. of Perpendiculars, 

fath. ft. in 

11 2 7.9231 
6 5 2.57466 


18 1 10.49776 
6 


A B.—52 ft. 11 in. 


AC.—109 ft. 10 in. 


EXAMPLE 5. 

ft hen a lode has changed or reversed, its underlay from north 
to south , or east to west. 

nr^.r E Tl dd k” the per P en(iicu!ars together, as in the last 
problem but subtract the bases, made by the reverse or con- 

rary shafts, one from the other, the remainder will be the 
true length of the bases. 

PROBLEM. 

A diagonal shaft was found to incline and 
lows, viz: 

g .. feet 18° 45' 

r n .. feet 12° J5' 

Throughout the above drafts the declination or underlay 
bote northerly, but from that depth, D, it made an angle 


measure as fol- 




























OWN BOOK AND GUIDE. 


41 


7° 30' in a southerly direction, and this last draft, D C, 



and bases of all the foregoing sides, respectively and col¬ 
lectively? 

OPERATION. 

Bases Northerly. Perpendiculars. 

/18° 45 / = f 0 h 1 11.14364 0 5 8.17897 

9 9 


A e 


Ba 2 5 4.29276 


8 3 1.61073 
















42 


THE PRACTICAL MINERS’ 


Z 12° 15'=0 1 

3.27680 

7 


0 5 10.36062 
7 

C b 12 

10.93760 

B b 

6 5 0.52434 

Z 25° 0'=0 2 

6.42852 

11 


0 5 5.25416 

11 

4 3 
0 1 

10.71372 

3.21426 


9 5 9.79576 
0 2 8.62708 

D c 4 5 

1.92798 


10 2 6.42284 

Base—Southerly. 

fath. ft. 

Z 7° 30'=0 0 

in. 

9.39789 

8 


fath. ft in. 

0 5 11.38483 

8 

1 0 

Ed 2 0 

3.18312 

2 

6.36624 

D d 

7 5 7.07224 

2 

15 5 2.14448 

SUMMARY. 

Bases. 

fath. ft. in 

2 5 4.29276 

1 2 10.93760 

4 5 1.92798 


Perpendicuars. 

8 3 1.61073 

6 5 0.52434 
10 2 6.42284 
15 5 2.14448 

North 9 1 

5.15834 


South 2 0 

6.36624 


41 3 10.70239 

7 0 

6 

10.79210 

0 

F E 249 ft. 10 in. 


F A 42 ft. 10 in. 


EXAMPLE 6. 

When a shaft has been sunk* in errror or not exactly at right 
angles with the lode. 

RULE I. 


Work for the base and perpendicular as before, by case one, 
then find the deviation by the following. 





















OWN BOOK AND GUIDE. 


43 


RULE II. 

Take out the base from the second table, standing opposite 
the angle of error, and multiply it by the length of the shaft* 

Underlaying shafts are always intended to be sunk at right 
angles with the lode, that is, if the lode runs east and west— 
the horizontal bearing of the shaft will be either north or 
south, as the lode may happen to underlie; but, it is some¬ 
times the case, that through inattention of workmen or other 
causes, the shaft has declined from its true course and inclined 
towards the right or left, and as this is neither a trivial nor 
uncommon occurrence, and admits not of development by the 
ordinary mode of surveying, we have here introduced a rule 
which will hold good in all cases of the kind. 

PROBLEM. 

An oblique shaft A B was found to measure 89 feet 6 inches, 
on an angle of 53° 15', and it was also observed that the shaft 
had declined 3° 45' west from the intended right angle of the 
east and west lode, required the base C D and perpendicular 
C A, and how far the shaft has departed from its true course 





44 


THE PRACTICAL MINERS’ 


OPERATION. 


/53° 15' 


ft. in. ft in. 



4 9.69027 

7 

3 

h 

3 7.07937 
7 


33 7.83189 



25 1.55557 


2 



2 


67 3.66378 



50 3.11118 


2 4.84513 



1 9.53968 


1 7.23009 

2 

i 

1 2.35979 


0 4.80722 

06 

i\ 

0 3.58994 


Base 71 8.54652 Perp. 53 6.60059 


THEN FOR THE DEVIATION. 


Table 2d.— /3° 45' Base 


ft. in. 


i 


0 4.7189 
7 


2 9.0323 
2 


5 6.0646 
0 2.3594 
I 0 0.78 
i 0.19 


5 9.3940 


1 lius it is clear that if the above shaft was sunk on an 
east and west lode, and the angle of error inclined westerly, 
that the foot of the shaft B would be 5 feet 9J inches in that 
direction beyond its designed course A D. 

EXAMPLE 7. 

To find the perpendicular depth of the junction of lodes. 

CASE i. 

When two lodes underlay in the same direction. 

Rule. Subtract the tabular number of the base of the 
lesser angle from the greater, then by direct proportion, say, 
























OWN BOOK AND GUIDE. 


45 


As this difference 

Is to one fathom perpendicular, 

So is the distance of the lodes at surface, 

To the junction of the lodes. 

PROBLEM. 

Two lodes were discovered at the surface, 12 fathoms apart 
from C to D, both underlaying north. The southernmost 
lode D B made an angle of 38° 15', the other, C B, 23° 
required the perpendicular depth, A B, where the lodes will 
unite, supposing they both regularly continue their respective 
angles of declination. 









46 


tiie practical miners’ 


OPERATION. 

ft. in. 

From / 38° 15 / =4 8.7602 
Take / 23° 0'=2 6.5622 


2 2.1980 


2 2.198 : 1 • 

: 12 

12 

6 

26.198 

72 


12 


26.198)864.000(32.9 
785 94 6 


78 060 5.4 
52 396 12 


25 6640 4.8 
23 5782 


2 0858 


fath. ft. in. 

Answer—32 5 4 A B. 










OWN BOOK AND GUIDE. 


4f 


DIAGONAL LODES. 

If it is required to find the respective lengths of the lodes C 
B and D B, and the horizontal line D A, work by case two, 
where the perpendicular is given. 

To find D B. 

/ 38° 15' I i 1 1 1 7.6831 Here we multiply by 33 

and subtract from the pro¬ 
duct what the hypothenuse 
is minus of that measure, 
which being eight inches, is 
one-ninth of a fathom.— 
This is the shortest method. 


1*1 ’ 

1 

7.6831 


11 

14 

0 

0.5141 



3 

42 

0 

1.5423 

0 

0 

10.1870 

DB 41 

5 

3.3553 


To find C B and D A, or C Jl. 


Base. 


Hypothenuse. 


/23° O' 


fath. 

ft. 

in. 

fath. 

ft. 

in. 

0 

2 

6.5622 


0 

6.2179 



11 

jij i 


11 

4 

4 

0.1842 

11 

5 

8.3969 



3 



3 

14 

0 

0.5526 

35 

5 

1.1907 

0 

0 

3.3964 

0 

0 

8.6908 

13 

5 

9.1580 

CB 35 

4 

4.4999 


Then C A+C D=D A, or C A added to C D gives the 
line D A, 25 fathoms, 5 feet, 9 inches, &c. 

EXAMPLE 8. 

To find the perpendicular depth of the junction of lodes. 

CASE II. 

When two lodes hy their underlay incline indirectly towards 
each other. 

Hule.—A dd the tabular bases together, then find the depth 
by direct proportion, as in the last example. 
















48 


THE PRACTICAL MINERS* 


PROBLEM. 

Two lodes were observed 36 fathoms apart at the surface 

lfiTtt‘° C ,’ ‘, he northernmost ^de, A, underlaying south 
’ and the southernmost lode, C, underlaying north 



31° 45', required the depth, B D, 
intersect each other ? 


at which these lodes will 


OPERATION. 


To 

Add 


/18° 15'=1 11.6220 

Z31°45'=3 8.5550 


5 8.177 














OWN BOOK AND GUIDE. 


49 


ft. in. 

Then, As 5 8.177 
12 


fath. 

1 


fath. 

36 

6 


68.177 


216 

12 


68.177)2592.0000(38.0 

204531 


546690 

545416 


12740 

Answer 38 fathoms. 

If required to find the length of the lodes A D and C D, 
and the distance of the shaft B, from the lodes C and A at the 
surface—work by case two, thus : 


Thus, to find A B and A V. 


Base. 


[Hypothenuse. 


fath. 

ft 

in. 




• 0 

1 

11.622 

1 

0 

3.8135 



6 



6 

1 

5 

9.732 

6 

1 

10.8810 



6 



6 

11 

4 

10.392 

37 

5 

5.2860 

0 

3 

11.244 

o 

0 

7.6270 

12 

2 

9.636 

; aD 40 

0 

0.9130 
















50 


THE PRACTICAL MINERS’ 


To find B C and C D. 

Base. Hypothenuse. 


fath. 

ft. 

in. 

fath. 

ft. 

in. 

1 45'— 0 

3 

8.555 

1 

1 

0.7008 



6 



6 

3 

4 

3.330 

7 

0 

4.2048 



6 



6 

22 

1 

7.980 

42 

2 

1.2288 

1 

1 

8.110 

2 

2 

1.4016 

B C* 23 

3 

1.090 

C D 44 

4 

2.6304 


PERPENDICULAR SHAFTS AND LEVELS. 

Rule.— When the angle of acclivity is given, take the 
complement, (or what it wants of 90°,) for the operative angle 
—in every other particular work by the former cases. 


A. 



* It may be observed that A B and B C added together do not make 
36 fathoms, by something more than an inch; now this does not happen 
through any defect in the tables, but because the perpendicular has not 
been worked out—for if the remainder, (12740,) was prosecuted, the 
perpendicular would prove to be 38 fath. 0 ft. 1.3392 in., instead of 38 
fathoms, which addition to multiplier would make up the exact defi¬ 
ciency. 


















OWN BOOK AND GUIDE. 


51 


EXAMPLE 1. 

A perpendicular shaft having been sunk from the top of a 
hill at A, from whence the slope to C measured 330 feet: It 
is required to know the length an adit must be driven from 
the base of the hill at C to intersect the shaft at B, and what 
will be the depth of the shaft at that intersection, the angle of 
acclivity at C being 41 degrees ? 


Comp, of 
41° is 49 


BY CASE II. 

Perpendicular, 
ft. in. 

3 11.23625 

9 

ft. 

4 

Base. 

in. 

6.33909 

9 

35 

5.12625 

6 

40 

9.05181 

6 

212 

6.75750 

244 

6.31086 

3 

11.23625 

4 

6.33909 

216 

5.99375 

249 

0.64995 



EXAMPLE 2. 

An adit having been driven 75 fathoms from A to B, re¬ 
quired to know how far up the hill from A, I ought to 
measure, in order that a perpendicular may be sunk to inter¬ 
sect the adit at x , 58 fathoms from the tail at A; also the 
depth of the shaft C x , the angle of acclivity from A towards 
C being 33 degrees. Or thus : Given the base 58 fathoms; 
angle of acclivity 33°, of which the complement or angle of 
declivity is 57°—required the hypothenuse and perpendicular? 














52 


THE PRACTICAL MINERS’ 


BY CASE III. 

Hypothenuse. 

ft. in. 

Comp. /33° is 57°== 7 1.85016 

8 


57 

2.80128 


7 

400 

7.60896 

14 

3.70032 

414 

11.30928 


EXAMPLE 3. 


From the foot of a perpendicular shaft, 
depth, a cross-cut was driven south 14 



Perpendicular. 

ft. in. 

3 10.75735 
8 


31 2.05880 

7 


218 241160 

7 9.51470 


225 11.92630 


A B, 70 fathoms in 
fathoms, 3 feet in 

D 
















OWN BOOK AND GUIDE. 


53 


length, (C,) where a lode was discovered underlaying north, 
and the angle of ascension or elevation 72° 45'—required the 
length of this lode from the end of the drift C to the surface 
D, also the distance from the brace of the perpendicular shaft 
A to the back of the lode at grass, (D,) supposing the lode to 
have a regular underlay ? 


BY case ii. 


Base. Hypothenuse. 


fath. ft. in. 

fath. ft. in. 

Comp, of > 0 1 10.3560 

1 0 3.3911 

/72° 45 / is 17° 15' J 7 

7 


2 

1 

0.4920 

7 

1 11.7377 



10 


10 

21 

4 

4.9200 

73 

1 9.3770 

14 

3 

0 







Add length of drift—36 1 4.92 


ANSWER. 

fath. ft. in. 

Length of lode.73 1 9£ 

Distance from shaft ? oe i tz 

at the surface. ) 


3 










54 


THE PRACTICAL MINERS 


EXAMPLE 4. 

Fom the depth of 36 fathoms, 4 feet, in 
an engine shaft A B, a cross-cut was 
driven, which pierced a lode, C, 14 fathoms, 
2 feet from B. The lode was found to 
make an angle of 30 degrees, inclining 
towards the shaft—required the depth at 
which the shaft will intersect the lode 
and the length of the lode from C to the’ 
point of intersection, O ? 



BY CASE III. 


Hypothenuse. 


Z 30° 


fath. 

ft. 

in. 

') 2 

0 

0 



2 

4 

0 

0 



7 

28 

0 

0 

0 

4 

0 


Perpendicular. 

fath. ft. in. 

i) 1 4 4.70766 
2 


3 

2 

9.41532 



7 

24 

] 

5.90724 

0 

3 

5.569 


28 4 0 


24 4 11.47624 













OWN BOOK AND GUIDE. 


55 


ANSWER. 

fath. ft. in. 

Depth from A to B.36 4 0 

Depth from B to 0.24 4 11.47624 

Extreme depth.61 2 11.47624 

Length from C to O... .28 fath. 4 ft. 


SLIDES. 

When a lode has been thrown up by a slide , to find the base 
and perpendicular. 

Rule.— Add the bases made by the segments of the lode 
together for the horizontal, and subtract the perpendicular 
made by the ascension of the slide, from the sum of the others 
for the perpendicular. 

EXAMPLE. 

A shaft having been sunk on a lode 114 feet from A to B, 
on an angle of 54° 30', at this place the lode was separated 
and thrown up by a slide, from B to C, 32 feet, the angle of 
elevation at B being 47°; at C, the lode was again cut and 
prosecuted on an angle of 51°, from C to D, 73 feet—required 
to know the length from A to E at surface, where a perpen¬ 
dicular shaft should be put down, that would intercept the 
lode at the foot of the diagonal, C D; also the depth of the 
shaft ED? 








56 


THE PRACTICAL MINERS’ 








OWN BOOK AND GUIDE. 


57 


The foregoing Examples by the table. 


Base. 


Perpendicular. 


ft. 

in. 

ft. 

in. 

Z A 54° 30'= 4 

10.61632 

3 

5.81062 

6 


6 

29 

3.69792 

20 

10.86372 ( Multiplier ) 


3 


3 J 19 faths. $ 

87 

11.09376 

62 

8.59116 

4 

10.61632 

3 

5.81062 

92 

9.71008 

66 

2.40178 


Base. 


Perpendicular. 


ft. in. 


ft. in. 

Zb 47° o'> |. 

i 1 4 1.10388 

1 i 

1 4 4.65747 

Comp. 43° 0' 5 — 1 

*1 s 

! 

5 


20 5.51940 


21 11.28735 C Multiplier ) 


1 4.36796 


1 5.5552 ( 5 fath. 2 ft. ) 


21 9.88736 


23 4.83935 

ft. : 

in. 


ft. in. 

Z c 51° 0' | £ | 4 

7.95451 

12 

1*1 

3 9.31107 

12 

55 1 

1.45412 


45 3.73284 C Multiplier ) 

0 

9.32575 


O 7.55184 1 12 fath. 1 ft. $ 

56 

8.77987 


45 11.28468 


SUMMARY. 


Bases. 


Perpendiculars. 

92 

9.71008 


ZA= 66 2 40178 

21 

9.88736 


ZC= 45 11.28468 

56 

8.77987 


112 1.68646 

Answer E A* 171 

4.37731 


ZB= 23 4.83935 


D E= 88 8.84711 


N 0XE .—Perpendiculars to strike B or C and their respective hori¬ 
zontal distances from A, are shown by the sums of the first and second 
operations in the above calculations. 





























58 


THE PRACTICAL MINERS’ 


When a lode has heen thrown down by a slide. 

Rule. —Add the perpendiculars together for the depth, and 
subtract the base of the slide from the bases of the segments 
of the lode for the horizontal. 

EXAMPLE. 

A shaft A B having been sunk 77 feet on a lode, which made 
an angle of 34° 45', it was there found that a slide had sever¬ 
al 



ed or disjointed the lode and carried it downward from B to C 
40 feet, on an angle of depression or declivity 59°, here, (at C,) 




OWN BOOK AND GUIDE. 


59 


the lode was again discovered, and wrought 102 feet from C 
to D, on an angle of 42° 15', required the depth of the verti¬ 
cal line D E, and length of the horizontal, A E ? 

The foregoing example by the table. 


Base. Perpendicular. 


/A, 34° 45' 

h 

ft. in. 

3 5.03977 

12 

i 

ft. in. 

4 11.15858 
12 


i 

41 0.47724 

1 8.51988 

1 1.67992 

i 

59 1.90296 

2 5.57929 

1 7.71952 



43 10.67704 


63 3.20177 

ZB, 59° 0' 

i 

ft in. 

5 1.71605 

6 

2 

ft. in. 

3 1.08274 

6 


i 

30 10.29630 

2 6.85802 

0 10.28600 

i 

18 6.49644 

1 6.54137 

0 6.18045 



34 3.44032 . 


20 7.21826 

ZC, 42° 15' 


ft. in. 

4 0.41041 

4 


ft. in. 

4 5.2957 

4 


16 

1.64164 

17 

9.1828 


4 


4 

64 

6.56656 

71 

0.7312 

4 

0.41041 

4 

5.2957 

68 

6.97697 

75 

6.0269 


]y 0TE ._Should it be required to find the proper depth in the shaft, 

D E, from whence to drive a cross-cut to strike the end of the shaft* 
A B, (where the slide first appeared,) the perpendicular of the first 

































6 0 


THE PRACTICAL MINERS’ 


ZA 

ZC 


ZB 


SUMMARY. 
Bases 
ft. in. 

43 10.67704 
68 6.97697 


112 5.65401 

34 3.44032 


Perpendiculars. 

ft. in. 

63 3.20117 
20 7.21826 
75 6.0269 


D E—159 4.44693 


Ans. A E= 78 2.21369 


HORIZONTAL SURVEYING. 

Rule.— Observe which side of the triangle is given, and 
work by the specifier! case. When there is more than one 
draft m the operation, add the sums of the respective sides to- 
gether for the answer. 

EXAMPLE 1. 

Being required to put down a shaft, 618 feet due east of an 
engine shaft at A, I am prevented from measuring in a direct 



d aft gives the depth, and the length of the cross-cut will be found by 

"a r " S - V baSe ° fthe firStdraft from(he horizontal line A E 
and should it be necessary to make a drift from the shaft, D E. to the 

angle, C, (where the lode was again discovered,) the depth will be 
found by adding the perpendiculars of A and B together and the bi 
ses of B and C will be the length of the drift. 
















OWN BOOK AND GUIDE. 


61 


line by intervening hills and wood, 1 therefore find it neces¬ 
sary, in order to avoid these obstructions, to go on an angle 
of 27° south of east from the shaft A. What distance must 
I proceed in this direction before I come at right angles with, 
or due south of the eastern extremity of the given line, and 
how far must I then measure in a northerly direction to come 
exactly on the required spot? Or, the question may stand 
thus: 

Given the perpendicular 618 feet, angle 27°; the hypothe- 
nuse and base are required? 

OPERATION. 

Base. Hypothenuse. 


ft. 

in. 

ft. 

in. 

3 

0.6858 

6 

8.8075 


10 


10 

30 

6.8580 

10 

67 

4.0750 

10 


Multiplier } 
103 fath. | 

i 305 

! 9 

8.5800 

2.0574 

673 

20 

4.7500 

2.4225 


314 10.6374 

693 

7.1725 


EXAMPLE 2. 

It being required to find the distance between two shafts, A 
and B, which are inaccessible to a direct measurement on ac¬ 
count of a marsh or lake lying in the way. I consequently 
measured 352 feet on an angle of 63°, south of west, from A 
to C; at this station, (C) 1 can see the shaft B, which I find 
by observation bears 29°, north of west, and the line from C 
to B, measures 615 feet; how far are these shafts apart in a 
right line? Or, the question may stand simply thus: 

( Given angle 63°, hypothenuse, 352 feet. ) 

| Given angle 29°, hypothenuse, 615 feet. $ 

The sum of the perpendiculars are required ?* 

*As in this instance the perpendicular only is wanted there is no 
necessity for taking out the other side. 

3* 











(Multiplier 58 fa. 4 ft.) 


62 


THE PRACTICAL MINERS 



C 


OPERATION. 


/A 63° 


1 

3 " 


Perpendicular. 

Perpendicular. 

ft. in. 

ft. in. 

2 8.68732 /_C 29° 

i 

5 2.97262 

11 


10 

29 11.56052 


52 5.72620 

5 


10 

149 9 80260 


524 9.26200 

8 2.06196 


10 5.94524 

1 4.34366 


2 7.48631 

0 5.44788 





537 10.69355 

159 9.65610 



SUMMARY. 

ft. in. 

159 9.65610 
537 10.69355 


Ans. A B. 697 8.34965 


(Multiplier 102 fa. 3 ft.) 





















OWN BOOK AND GUIDE. 


63 


VERTICAL SURVEYING 

OR THE 

MENSURATION OF HEIGHTS. 


Rule.—O bserve the given side and angle, and work by the 
respective cases as heretofore. 


C 



From the bottom of a tower at B, I measured 200 feet in 
a direct line, B A, on an horizontal plane, I then took the an¬ 
gle A, 42°; required the height of the tower and staff B C ? 

OPERATION. 

ft. in. 


Complemen of /_k > 
42°, is /C, 48°. J 



5 4.82909 

11 


59 5.11999 
3 


Multiplier ) 
53 fath. 2 ft. } 


178 3.35997 
1 9.60969 

Ans. B C. 180 0.96966 


In operations of this nature the hypothenuse need not be 
regarded. 



















64 


THE PRACTICAL MINERS’ 


EXAMPLE 2. 

Wanted* to ascertain the height of an irregular hill, I pro¬ 
ceed, from the several stations, A, B, and C, to take the angles 
and measure the distances as follows, viz: 

From A to B, /41° O', length 210 feet. 

From B to C, /22° O', length 216 feet. 

From C to D, /37° 30', length 247 feet. 

R equired the altitude E D? 


I) 



OPERATION. 


ZA, 41° O', comp. 49° O' 
6)210 feet. 

35 Multiplier. 


ZB, 22° O', comp. 68° 0' 
6)216 

36 Multiplier. 


Perpendicular. 


ft. 

3 

in. 

11.23625 

7 

27 

6.65375 

5 

137 

9.28675 

2 

2.97167 

6 

13 

5.83002 

6 

80 

10.98012 

















OWN BOOK AND GUIDE. 

ZC, 37° 30% comp. 52° 30', 

6)247 

41.1 Multiplier. 


65 


3 

7.83082 

10 

36 

6.30820 

4 

146 

1.23280 

3 

7.83082 

0 

7.30513 

150 

4.36875 


ft. in. 

A 137 9.26875 

B 80 10.98012 

C 150 4 36875 

Ans. Height, E D 369 0.61762 

Miscellaneous examples in the foregoing rules. 

Given the hypothenuse, 14 feet 5 inches, angle 88°; re¬ 
quired the base and perpendicular?* 

ft. in. 

. $ Base =14 4.89 

Ans * I Perp.= 0 6.03 

Given the perpendicular, 100 feet, angle 60°; required the 
hypothenuse and base ? 

ft. in. 

. ( Hvp. =200 

Ans * l Base =173 2.428 

Given the base, 118 feet, angle (comp.) 23°; required the 
hypothenuse and perpendicular? 

ft. in. 

. (Hyp.—301 11.97 
Ans ' | Perp.—278 0.02 

Given the angle 53°; required the underlay in a fathom ?| 
Ans. 1 fath. 1 ft. 11.5472 in. 


*In single drafts, one or two figures of the decimal will be sufficient, 
the others may be rejected. 

|It has been before observed that the underlay is given in the base 
of the second table. 












66 


THE PRACTICAL MINERS 


Given the angle 36° 45'; required the underlay in a fa¬ 
thom ? 

Ans. 4 ft. 5.5650 in. 

Given the angle 4° 15'; required the underlay in a fathom? 

Ans. 5.3496 in. 

A diagonal shaft having been sunk 8° 30' out of its true 
course, what will be the extent of departure, supposing the 
length of the shaft 76 feet ? 

Ans. 11 ft. 4.9577 in. 

Suppose a diagonal shaft was sunk as follows, viz : 

Z87° 0'=14 5 
Z 47 ° 0'=11 2 
/87° 30'=36 3 
Z69° 30 / =26 2 
Z 77° 30'=23 2 y 
Z65° 30'= 9 2 

Required the sum of the bases and perpendiculars ? 

An _ $Perp.= 52 8.45944 
) Bases=169 6.90784 

Wanting to know the distance between two shafts, inacces¬ 
sible in a right line, I measured from the first shaft 126 feet, 
on an angle of 27° 15' E. by N.; from this station to the se¬ 
cond shaft the line measured 91 feet, on an angle of 42° 30' 
N. by W.; how far are the shafts apart? 

Ans. 179 ft. 1.3 in. 

Wanting to know the altitude of a precipice, I measure off 
from its base 66 feet, and from thence J take the angle to the 
summit, which 1 find to be 42°, (and consequently the com¬ 
plement 48°;) required the height ? 

Ans. 59 ft. 5.91999 in. 

At the foot of a hill the angle to the summit was 36°, from 
this place an adit had been driven in a direct line 218 feet; 
how far must I measure up the hill to put down a perpendic¬ 
ular on the end of the adit, and what will be the depth of the 

s ^ t? A ng $ Hyp. or slope 281 5.54804 

' l Perp. or shaft 158 4.62816 


OWN BOOK AND GUIDE. 


67 


At the foot of a diagonal shaft, 28 fathoms in length, sunk 
on a lode 27° 45', underlaying north, another lode was cut 
making an angle 48° 45', underlaying south ; what is the dis¬ 
tance from the brace of the shaft to the back of the north 
lode ? 


/ 27 ° 4 5 ' 


FIRST TABLE. 


Base. 

Perp. 

ft. in. 

ft. in. 

2 9.5 

5 3.7 

7 

7 

19 6.5 

37 1.9 

4 

4 

78 2.0 

148 7.6 


148 ft. 7.6 in.—Divide this byj6, for the multiplier of the 
second angle, which will be 24 fath. 4 ft. 7.6 in. 


Then, 

/48° 45' } 
comp. > 
41° 15'. ) 

i 

SECOND 

Base, 
ft. in. 

5 3.14 
6 


31 6.84 
4 


3 

8 

126 3.36 
2 7.57 
0 10.52 
0 5.26 
0 0.65 



130 3.36 


TABLE. 


Answer. 

ft. in. 

Base of north lode 78 2 
Base of south lode 130 3 


Required distance 208 5 


A perpendicular shaft having been sunk 168 feet in the side 
of a mountain, the slope or declivity making an angle with the 
shaft of 54° 15', required to know how far I must measure 
down the hill to get at the right spot for driving an adit to 
come in the exact depth of the shaft; the length of the adit is 
also required. 


Ans. 


Slope 287 8.58 
Adit 233 4.40 















68 


THE PRACTICAL MINERS’ 


A lode underlaying south was observed to make an angle of 
17° 15', required to know what distance from the back of 
the lode will be proper for sinking a perpendicular shaft, that 
shall intersect the lode at the depth or 45 fathoms ? 

Ans. 83 ft. 10.020 in. 


















OWN BOOK AND GUIDE. 


69 


FIRST TABLE. 

HYPOTHENUSE RADIUS. 

ONE FATHOM. 


ANGLE. 

BASE. 

PERPENDICULAR. 

Deg. 

Min. 

Feet. 

Ins. 

Decimals. 

Feet. 

Ins. 

1 

Decimals. 1 

Deg. 

Min. 


1 

0 

0 

.02094 

1 

6 

0 


89 

59 


2 

0 

0 

.04189 

6 

0 


89 

58 


3 

0 

0 

.06283 

6 

0 


89 

57 


4 

0 

0 

.08387 

6 

0 


89 

56 


5 

0 

0 

.10482 

6 

0 


89 

55 


6 

0 

0 

.12576 

6 

0 


89 

54 


7 

0 

0 

.14670 

6 

0 


89 

53 


8 

0 

0 

.16765 

6 

0 


89 

52 


9 

0 

0 

.18859 

6 

0 


89 

51 


10 

0 

0 

.20943 

6 

0 


89 

50 


11 

0 

0 

.23038 

6 

0 


89 

49 


12 

0 

0 

.25132 

6 

0 


89 

48 


13 

0 

0 

.27225 

6 

0 


89 

47 


14 

0 

0 

.29319 

6 

0 


89 

46 


15 

0 

0 

.31414 

5 

11 

.99932 

89 

45 


30 

0 

0 

.62831 

5 

11 

.99726 

89 

30 


45 

0 

0 

.94245 

5 

11 

.99381 

89 

15 

PERPENDICULAR. 

BASE. 

ANGLE. 


Note. — I hope this table will be found useful in particular cases 
for long lines where the angle is required to be very minute. It will 
he seen that as there is but the thousandth part of an inch difference in 
one fathom, between the hypothenuse and perpendicular on the first 
15' or first { of a degree, the introduction of the decimal at any less 
fraction would be useless. 





















































70 


the practical miners’ 

FIRST TABLE.—HYPOTHENUSE RADIUS. 


1 ANGLE. 

BASE. 

PERPENDICULAR. 

Deg. 

Min. 

Fee 

• Ins. 

Decimals. 

Feel 

t. Ins. 

Decimals. 

Deg. 

Min. 

1 


0 

1 

.25657 

5 

11 

.98903 

89 



16 

0 

1 

.57067 

5 

11 

.98286 


45 


30 

0 

1 

.88474 

5 

11 

.97532 


30 


45 

0 

2 

.19877 

5 

11 

.96664 


]5 

2 


0 

2 

.51276 

5 

11 

.95614 

88 



15 

0 

2 

.82666 

5 

11 

.94249 


45 


30 

0 

3 

.14060 

5 

11 

.93147 


30 


45 

0 

3 

.45442 

5 

11 

.91708 


15 

3 


0 

3 

.76819 

5 

11 

.90132 

87 



15 

0 

4 

.08188 

5 

11 

.88420 


45 


30 

0 

4 

.39549 

5 

11 

.86571 


30 


45 

0 

4 

.70902 

5 

11 

.84584 


15 

4 


0 

5 

.02246 

5 

11 

.82461 

86 



15 

0 

5 

.33581 

5 

11 

.80201 


45 


30 

0 

5 

.64905 

5 

11 

.77805 


30 


45 

0 

5 

.96219 

5 

11 

.75272 


15 

5 


0 

6 

.27521 

5 

11 

.72602 

85 



15 

0 

6 

.58811 

5 

11 

.69793 


45 


30 

0 

6 

.90090 

5 

11 

.66853 


30 


45 

0 

7 

.21354 

5 

11 

.63773 


15 

6 


0 

7 

.52605 

5 

11 

.60558 

84 



15 

0 

7 

.83842 

5 

11 

.57205 


45 


30 

0 

8 

.15063 

5 

11 

.53718 


30 


45 

0 

8 

.46269 

5 

11 

.50093 


15 

7 


0 

8 

.77459 

5 

11 

.46333 

83 



15 

0 

9 

.08633 

5 

11 

.42435 


45 


30 

0 

9 

.39789 

5 

11 

.38403 


30 


45 

0 

9 

.70926 

5 

11 

.34234 


15 

8 


0 

10 

.02046 

5 

11 

.29930 

82 



15 

0 

10 

.33147 

5 

11 

.25490 


45 


30 

0 

10 

.64228 

5 

11* 

.20914 


30 


45 

0 

10 

.95288 

5 

11 

.16203 


15 

9 


0 

11 

.26328 

5 

11 

.11356 

81 



lo 

0 

1] 

.57347 

5 

11 

.06374 


45 


30 

0 

11 

.88343 

5 

11 

.01256 


30 

10 

45 

0 

0 

.19316 

5 

10 

.96004 


15 

1 

0 

o 

.50267 

5 

10 

.90616 

80 


perpendicular. 

BASE. 1 

ANGI. 

E. 



















































































OWN BOOK AND GUIDE. 


71 


FIRST TABLE.—HYPOTHENUSE RADIUS. 


ANGLE. 

BASE. 

PERPENDICULAR. 

Deg. 

Min. 

Feet. 

Ins. 

Decimals. 

Feet. 

Ins. 

Decimals. 1 

Deg. 1 

Min. 

10 

15 

1 

0 

81193 

5 

10 

.85093 


45 


30 

1 

1 

.12096 

5 

10 

.79435 


30 


45 

1 

1 

.42973 

5 

10 

.73643 


15 

11 


1 

1 

.73825 

5 

10 

.67716 

79 



15 

1 

2 

.04650 

5 

10 

.61654 


45 


30 

1 

2 

.35449 

5 

10 

.55458 


30 


45 

1 

2 

.66221 

5 

10 

.49128 


15 

12 


1 

2 

.96964 

5 

10 

.42663 

78 



15 

1 

3 

.27680 

5 

10 

.36062 


45 


30 

1 

3 

58365 

5 

10 

.29331 


30 


45 

1 

3 

.89021 

5 

10 

.22464 


15 

13 


1 

4 

.19648 

5 

10 

.15465 

77 


15 

1 

4 

.50243 

5 

10 

.08331 


45 


30 

1 

4 

.80807 

5 

10 

.01062 


30 


45 

1 

5 

.11338 

5 

9 

.93663 


15 

14 


1 

5 

.41838 

5 

9 

.86129 

76 


15 

1 

5 

.72204 

5 

9 

.72304 


45 


30 

1 

6 

.02736 

5 

9 

.70663 


30 


45 

r 

6 

.33134 

5 

9 

.62730 


15 

15 


i 

6 

.63497 

5 

9 

.54666 

75 


15 

i 

6 

.93825 

5 

9 

.46469 


45 


30 

i 

7 

.24116 

5 

9 

.38139 


30 


45 

i 

7 

.54371 

5 

9 

.29677 


15 

16 

i 

7 

.84589 

5 

9 

.21084 

74 


15 

i 

8 

.14769 

5 

9 

.12359 


45 


30 

i 

8 

.44910 

5 

9 

.03502 


30 


45 

i 

8 

.75014 

5 

8 

.94514 


15 

17 

i 

9 

.05076 

5 

8 

.85395 

73 


15 

i 

9 

.35099 

5 

8 

.76143 


45 


30 

i 

9 

.65082 

5 

8 

.66762 


30 


45 

i 

9 

.95023 

5 

8 

.57250 


15 

18 

i 

10 

.24922 

5 

8 

.47607 

72 


15 

i 

10 

.54779 

5 

8 

.37833 


45 


30 

i 

10 

.84594 

5 

8 

.27931 


30 


45 

i 

11 

.14364 

5 

8 

.17897 


15 

19 

i 

11 

.44091 

5 

8 

.07734 

71 


15 

i i 

11 

.73772 

5 

7 

.97441 


45 

PERPENDICULAR. 

BASE. 

ANGLE. 






























































72 


THE PRACTICAL MINERS' 

FIRST TABLE.—HYPOTHENUSE RADIUS. 


ANGLE. 

BASE. 

PERPENDICULAR. 

Deg 

Min 

Fee 

t. Ins 

Decimals. 

Fee 

t. Ins. 

Decimals, 

Deg, 

. Min. 

19 

30 

2 

0 

.03409 

5 

7 

.87019 


30 


45 

2 

0 

.33000 

5 

7 

.76467 


15 

20 


2 

0 

.62545 

5 

7 

.65787 

70 



15 

2 

0 

.92043 

5 

7 

.54977 


45 


30 

2 

1 

.21493 

5 

7 

.44040 


30 


45 

2 

1 

.50895 

5 

7 

.32973 


15 

21 


2 

1 

.80249 

5 

7 

.21779 

69 



It) 

2 

2 

. 09554 

5 

7 

.10457 


45 


30 

2 

2 

.38809 

5 

6 

.99007 


30 


45 

2 

2 

.68013 

5 

6 

.87429 


15 

22 


2 

o 

.97167 

5 

6 

.75724 

68 



15 

2 

3 

.26270 

5 

6 

.63892 


45 


30 

2 

3 

.55320 

5 

6 

.51932 


30 


45 

2 

3 

.84320 

5 

6 

.39847 


15 

23 


2 

4 

.13264 

5 

6 

.27635 

67 



15 

2 

4 

.42156 

5 

6 

.15297 


45 


30 

2 

4 

.70993 

5 

6 

.02833 


30 

A 

45 

2 

4 

.99776 

5 

5 

.90^43 


15 

24 


2 

5 

.28503 

5 

5 

.77528 

66 



15 

2 

5 

.57176 

5 

5 

.64686 


45 


30 

2 

5 

.85791 

5 

5 

.51721 


30 


45 

2 

6 

.14350 

5 

5 

.38631 


15 

2 5 


2 

6 

.42852 

5 

5 

.25416 

65 



15 

2 

6 

.71295 

5 

5 

.12077 


45 


30 

2 

6 

.99681 

5 

4 

.98614 


30 


45 

2 

7 

.28006 

5 

4 

.85027 


15 

26 


2 

7 

.56272 

5 

4 

.71317 

64 

At/ 


15 

2 

7 

.84479 1 

5 

4 

.57483 


45 


30 

2 

8 

.12622 1 

5 

4 

.43528 1 


30 

r\ ry 

45 

2 

8 

.40708 

5 

4 

.29448 


15 

2/ 


2 

8 

.68732 

5 

4 

.15247 

63 


15 

2 

8 

.96692 

5 

4 

.00923 


45 


30 

2 

9 

.24590 

5 

3 . 

.86478 


30 

no 

45 

2 

9 

.52424 

5 

3 . 

.71911 


15 

28 


2 

9 . 

80195 

5 

3 .57223 

62 


15 

2 

10 . 

07902 

5 

3 .42413 


15 

30 

_ 

30 

2 1 

10 . 

35543 

5 

3 .27483 

i 

perpendicular. 1 

BASE. 

i 

ANGLl 

E. 




























































































OWN BOOK AND GUIDE. 


73 


FIRST TABLE.—HYPOTHENUSE RADIUS. 


ANGLE. 

BASE. 

PERPENDICULAR. 

Deg. 

Min. 

Feet. 

Ins. 

Decimals. 

Feet. 

Ins. 

Decimals. 

Deg. 

Min. 

28 

45 

2 

10 

.63120 

5 

3 

.12433 


15 

29 


2 

10 

.90630 

5 

2 

.97262 

61 



15 

2 

11 

.18073 

5 

2 

.81972 


45 


30 

2 

11 

.45450 

5 

2 

.66561 


30 


45 

2 

11 

.72759 

5 

2 

.51031 


15 

30 


3 

0 

.00000 

5 

2 

.35383 

60 



15 

3 

0 

.27173 

5 

2 

.19616 


45 


30 

3 

0 

.54276 

5 

2 

.03730 


30 


45 

3 

0 

.81310 

5 

1 

.87726 


15 

31 


3 

1 

.08274 

5 

1 

.71605 

59 



15 

3 

1 

.35168 

5 

1 

.55366 


45 


30 

3 

1 

.61990 

5 

1 

.39009 


30 


45 

3 

1 

.88740 

5 

1 

.22536 


15 

32 


3 

2 

.15419 

5 

1 

.05946 

58 


15 

3 

2 

.42024 

5 

0 

.89240 


45 


30 

3 

2 

.68557 

5 

0 

.72418 


30 


45 

3 

2 

.95016 

5 

0 

.55481 


15 

33 


3 

3 

.21401 

5 

0 

.38428 

57 


15 

3 

3 

.47711 

5 

0 

.21261 


45 


30 

3 

3 

.73946 

5 

0 

.03978 


30 


45 

3 

4 

.00105 

4 

11 

.86581 


15 

34 


3 

4 

.26189 

4 

11 

.69071 

56 


15 

3 

4 

.52195 

4 

11 

.51446 


45 


30 

3 

4 

.78125 

4 

11 

.33709 


30 


45 

3 

5 

.03977 

4 

11 

.15858 


15 

35 


3 

5 

.29750 

4 

10 

.97894 

55 


15 

3 

5 

.55445 

4 

10 

.79819 


45 


30 

3 

5 

.81062 

4 

10 

.61632 


30 


45 

3 

6 

.06598 

4 

10 

.43333 


15 

36 


3 

6 

.32054 

4 

10 

.24922 

54 


15 

3 

6 

.57429 

4 

10 

.06401 


45 


30 

3 

6 

.82724 

< 4 

9 

.87770 


30 


45 

3 

7 

.07937 

4 

9 

.69027 


15 

37 

3 

7 

.33068 

4 

9 

.50176 

53 


15 

3 

7 

.58117 

4 

9 

.31214 


45 


30 

3 

7 

.83082 

4 

9 

.12144 


30 


45 

3 

8 

.07965 

, 4 

8 

.92965 


15 

PERPENDICULAR. 

BASE. 

ANGLE. 












































74 THE PRACTICAL MINERS’ 


FIRST TABLE.—HYPOTHENUSE RADIUS. 


ANGLE. 

1 

BASE. 

PERPENDICULAR. 

Deg. 

Min. 

Feet 

Ins. 

Decimals. 

Feet 

Ins. 

Decimals. 

Deg. 

Min. 

38 

15 

3 

8 

.32763 

4 

8 

.73678 

52 



3 

8 

.57476 

4 

8 

.54282 


45 


30 

3 

8 

.82105 

4 

8 

.34779 


30 

39 

45 

3 

9 

.06649 

4 

8 

.15168 


15 


3 

9 

.31307 

4 

7 

.95451 

51 



15 

3 

9 

.55478 

4 

7 

.75627 

45 


30 

3 

9 

.79763 

4 

7 

.55697 


30 

40 

45 

3 

30 

.03961 

4 

7 

.35661 


15 


3 

10 

.28071 

4 

7 

.15520 

50 


15 

3 

10 

.52093 

4 

6 

.95274 

45 


30 

3 

10 

.76026 

4 

6 

.74923 


30 

41 

45 

3 

10 

.99871 

4 

6 

.54468 


35 

15 

3 

11 

.23625 

4 

6 

.33909 

49 


3 

11 

.47290 

4 

6 

.13246 

45 


30 

3 

11 

.70864 

4 

5 

.92481 


30 

42 

45 

3 

11 

.94348 

4 

5 

.71613 


15 

15 

4 

0 

.37740 

4 

5 

.50643 

48 


4 

0 

.41041 

4 

5 

.29570 

45 


30 

4 

0 

.64250 

4 

5 

.08396 


30 

43 

45 

4 

0 

.87365 

4 

4 

.87122 


15 

15 

4 

1 

.10388 

4 

4 

.65747 

47 


4 

1 

.33318 

4 

4 

.44271 

45 


30 

4 

1 

.56153 

4 

4 

.22696 


30 

44 

45 

4 

1 

.78894 

4 

4 

.01021 


15 

15 

4 

2 

.01540 

4 

3 

.79247 

46 


4 

2 

.24092 

4 

3 

.57374 

45 


30 

4 

2 

.46541 

4 

3 

.35403 


30 

45 

45 

4 

2 

.68906 

4 

3 

.13335 


15 


4 

2 

.91169 

4 

2 1 

.91169 

45 

PERPENDICULAR. 

BASE. | 

ANGLE. 






























































OWN BOOK AND GUIDE. 




pa. 










THE PRACTICAL MINERS’ 


76 


SECOND TABLE. 
PERPENDICULAR RADIUS. 


ONE FATHOM. 


ANGLE. 

BASE. 

HYPOTHENUSE. 

Deg. 

Min. 

Fath. 

Feet. 

Ins. 

Decimals. 

Fath. 

Feet. 

Ins. 

Decimals. 

1 



0 

1 

•2568 

1 

0 

0 

.0108 


15 

0 

0 

1 

.5710 

1 

0 

0 

.0171 


30 

0 

0 

1 

.8854 

1 

0 

0 

.0247 


45 

0 

0 

2 

.1998 

1 

0 

0 

.0335 

2 


0 

0 

2 

.5143 

1 

0 

0 

.0432 


15 

0 

0 

2 

.8289 

1 

0 

0 

.0554 


30 

0 

0 

3 

.1435 

1 

0 

0 

.0684 


45 

0 

0 

3 

.4582 

1 

0 

0 

.0828 

3 


0 

0 

3 

.7728 

1 

0 

0 

.0986 


15 

0 

0 

4 

.0882 

1 

0 

0 

.1159 


30 

0 

0 

4 

.4035 

1 

0 

0 

.1346 


45 

0 

0 

4 

.7189 

1 

0 

0 

.1544 

4 


0 

0 

5 

.0328 

1 

0 

0 

.1757 


15 

0 

0 

5 

.3496 

1 

0 

0 

.1980 


30 

0 

0 

5 

.6664 

1 

0 

0 

.2171 


45 

0 

0 

5 

.9825 

1 

0 

0 

.2484 

5 


0 

0 

6 

.2993 

1 

0 

0 

.2736 


15 

0 

0 

6 

.6168 

1 

0 

0 

.3024 


30 

0 

0 

6 

.9336 

1 

0 

0 

.3312 


42 

0 

0 

7 

.2497 

1 

0 

0 

.3636 

6 


0 

0 

7 

.5672 

1 

0 

0 

.3960 


15 

0 

0 

7 

.8841 

1 

0 

0 

.4298 


30 

0 

0 

8 

.2008 

1 

0 

0 

.4658 


45 

0 

0 

8 

.5212 

1 

0 

0 

.5026 

7 


0 

0 

8 

.8402 

1 

0 

0 

.5400 


15 

0 

0 

9 

.1584 

1 

0 

0 

.5803 


30 

0 

0 

9 

.4788 

1 

0 

0 

.6192 


45 

0 

0 

9 

.7992 

1 

0 

0 

.6624 

8 


0 

0 

10 

.1189 

1 

0 

0 

.7056 


15 

0 

0 

10 

.4393 

1 

0 

0 

.7531 


30 

0 

0 

10 

.7604 

1 

0 

0 

.7992 


45 

0 

0 

11 

.0808 

1 

0 

0 

.8474 









































OWN BOOK AND GUIDE. 7^ 


SECOND TABLE.—PERPENDICULAR RADIUS. 


ANGLE. 

BASE. 

HYPOTHENUSE. 

Deg. 

Min. 

Falh. 

j Feet 

. Ins. 

Decimals. 

Fath. 

Feet 

. Ins. 

Decimals. 

9 


0 

1 0 

11 

.4034 

1 

0 

0 

.8971 


15 

0 

1 0 

11 

.7259 

1 

0 

0 

.9482 


30 

0 

1 

0 

.0485 

1 

0 

1 

.0008 


45 

0 

1 

0 

.3696 

! 1 

0 

1 

.0548 

10 


0 

1 

0 

.6936 

1 

0 

1 

.1088 


15 

0 

1 

1 

.0176 

1 

0 

1 

.1664 


30 

0 

1 

1 

.3416 

1 

0 

1 

.2262 


45 

0 

1 

1 

.6692 

1 

0 

1 

.2859 

11 


0 

1 

1 

.9954 

1 

0 

1 

.3476 


15 

0 

1 

2 

.3215 

1 

0 

1 

.4106 


30 

0 

1 

2 

.6484 

1 

0 

1 

.4750 


45 

0 

l 

2 

.9760 

1 

0 

1 

.5410 

12 


0 

1 

3 

.3036 

1 

0 

1 

.6085 


15 

0 

1 

3 

.6326 

1 

0 

1 

.6775 


30 

0 

1 

3 

.9617 

1 

0 

1 

.7481 


45 

0 

1 j 

4 

.2914 

1 

0 

1 

.8202 

13 


0 

1 

4 

.6219 

1 

0 

1 

.8939 


15 

0 

1 

4 

.9538 

1 

0 

1 

.9691 


30 

0 

1 

5 

.2857 

1 

0 

2 

.0459 


45 

0 

1 

5 

.6178 

1 

0 

2 

.1242 

14 


0 

1 

5 

.9496 

1 

0 

2 

.2042 


15 

0 

1 

6 

.2858 

1 

0 

2 

.2857 


30 

0 

1 

6 

.6192 

1 

0 

2 

.3688 


45 

0 

1 

6 

.9576 

1 

0 

2 

.4535 

15 


0 

1 

7 

.2888 

1 

0 

2 

.5399 


15 

0 

1 

7 

.6294 

1 

0 

2 

.6338 


30 || 

0 

1 

7 

.9670 

1 

0 

2 

.7174 


45 1 

0 

1 

8 

.3062 

1 

0 

2 

.8087 

1G 


0 

1 

8 

.6456 

1 

0 

2 

.9015 


15 II 

0 

1 

8 

.9858 

1 

0 

2 

.9961 


30 

0 

1 

9 

.3271 

1 

0 

3 

.0443 


45 

0 

1 

9 

.6695 

1 

0 

3 

.1902 

17 


0 

1 

10 

.0126 

1 

0 

3 

.2898 


15 

0 

1 

10 

.3560 | 

1 

0 

3 

.3911 


30 

0 

1 

10 

.7003 1 

1 

0 

3 

.4941 


45 

0 

1 

1 

.0472 

1 

0 

3 

.5988 

18 


0 

1 

11 

.3942 ! 

1 

0 

3 

.7053 


4 









































































78 


THE PRACTICAL MINERS’ 

SECOND TABLE.—PERPENDICULAR RADIUS. 


ANGLE. 

BASE. 

HYPOTHENUSE. 

Deg. 

Min. 

Fath. 

Feet. 

Ins. 

Decimals. ; 

j Fath. 

Feet. 

Ins. 

Decimals. 

18 

15 

0 

1 

11 

.6220 1 

1 1 

0 

3 

.8135 


30 

0 

2 

0 

.0905 

j 1 

0 

3 

.9234 


45 

0 

2 

0 

.4204 ; 

1 

0 

4 

.0352 

19 


0 

2 

0 

.7916 

j 1 

0 

4 

.1487 


15 

0 

2 

1 

.1435 

1 

0 

4 

.2640 


30 

0 

2 

1 

.4965 

1 

0 

4 

.3811 


45 

0 

2 

1 

.8506 

1 

0 

4 

.5000 

20 


0 

2 

2 

.2058 

1 

0 

4 

.6208 


15 

0 

2 

2 

.5622 

1 

0 

4 

.7434 


30 

0 

2 

2 

.9197 

1 

0 

4 

.8679 


45 

0 

2 

3 

.2783 

1 

0 

4 

.9942 

21 


0 

2 

3 

.6262 I 

1 

0 

5 

.1224 


15 

0 

2 

3 

.9993 

1 

o j 

5 

.2526 


30 

0 

2 

4 

.3615 

1 

0 

5 

.3846 


45 

0 

2 

4 

.7251 

1 

0 

5 

.5186 

| 22 


0 

2 

5 

.0899 

1 

0 

5 

.6545 


15 

0 

2 

5 

.4560 i 

1 

0 

5 

.7924 


30 

0 

2 

5 

.8234 j 

1 

0 

5 

.9323 


45 

0 

2 

6 

.1921 i 

1 

0 

6 

.0741 

23 


0 

2 

6 

.5622 | 

1 

0 

6 

.2179 


15 

0 

2 

6 

.9336 

1 

0 

6 

.3638 


30 

0 

2 

7 

.3065 

I 

0 

6 

.5117 


45 

0 

o 

7 

.6807 ! 

] 

0 

(j 

.6617 

24 


1 0 

2 

8 

.0565 ' 

1 

0 

6 

.8138 


15 

~ ~ 1 

0 

2 

8 

.4336 

1 

0 

6 

.9679 


30 

0 

2 

8 

.8123 

1 1 

0 

7 

.1242 


45 

0 

2 

9 

.1924 

1 1 

0 

7 

.2826 

25 


0 

2 

9 

.5741 

1 

0 

7 

.4432 


15 

0 

2 

9 

.9574 

1 

0 

7 

.6059 


30 

0 

2 

ib 

.3422 

1 

0 

7 

.7708 


45 

0 

2 

10 

.7287 

1 

0 

7 

.9380 

26 


0 

2 

11 

.1167 

1 

0 

8 

.1073 


15 

0 

2 

11 

.5065 

1 

0 

8 

.2789 


30 

0 

2 

11 

.8979 

1 

0 

8 

.4528 


45 

0 

3 

0 

.2910 

1 

0 

8 

.6290 

27 


0 

3 

0 

.6858 

1 

0 

8 

.8075 


15 

0 

3 

1 

.0824 

1 

0 

8 

.9883 







































































OWN BOOK AND GUIDE. 


79 


SECOND TABLE.—PERPENDICULAR RADIUS. 


ANGLE. 

BASE. 

HYPOTHENUSE. 

Deg. 

Min. 

Fath. 

Feet. 

Ins. 

i 

Decimals. 

Fath. 

Feet. 

Ins. 

Decimals. 

27 

30 

0 

3 

1 

.4808 

1 

0 

9 

.1714 


45 

0 

3 

1 

.8810 

1 

0 

9 

.3571 

28 


0 

3 

2 

.2831 

1 

0 

9 

.5450 


15 

0 

3 

2 

.6870 

1 

0 

9 

.7354 


30 

0 

3 

3 

.0928 

1 

0 

9 

.9283 


45 

0 

3 

3 

.5005 

1 

0 

10 

.1232 

29 


0 

3 

3 

.9102 

1 

0 

10 

.3212 


15 

0 

3 

4 

.3219 

1 

0 

10 

.5220 


30 

0 

3 

4 

.7356 

1 

0 

10 

.7251 


45 

0 

3 

5 

.1514 

1 

0 

10 

.9303 

30 


0 

3 

5 

.5692 

1 

0 

11 

.1384 


15 

0 

3 

5 

.9892 

1 

0 

11 

.3494 


30 

0 

3 

6 

.4112 

1 

0 

11 

.5625 


45 

0 

3 

6 

.8355 

1 

0 

11 

.7788 

31 


0 

3 

7 

.2620 

1 

0 

11 

.9976 


15 

0 

3 

7 

.6907 

1 

1 

0 

.2192 


30 

0 

3 

8 

.1216 

1 

1 

0 

.4436 

# 

45 

0 

3 

8 

.5550 

1 

1 

0 

.7008 

32 


0 

3 

8 

.9906 

1 

1 

0 

.9008 


15 

0 

3 

9 

.4286 

1 

1 

1 

.1338 


30 

0 

3 

9 

.8691 

1 

1 

1 

.3696 


45 

0 

3 

10 

.3119 

1 

1 

1 

.6084 

33 


0 

3 

10 

.7573 

1 

1 

1 

.8501 


15 1 

0 

3 

11 

.2053 

1 

1 

2 

.0949 


30 

0 

3 

11 

.6558 

i 1 

1 

2 

.3427 


45 

0 

4 

0 

.1088 

1 

1 

2 

.5937 

34 


0 

4 

0 

.5646 

1 

1 

2 

.8477 


15 

0 

4 

0 

.9931 

1 

1 

3 

.1049 


30 [ 

0 

4 

1 

.4842 | 

1 

1 

3 

.3653 


45 

0 

4 

1 

.9482 

1 1 ! 

1 

3 

.6289 

35 


0 

4 

2 

.4149 | 


1 

3 

.8958 


15 

o 

4 

o 

.8846 

! i 

1 

4 

.1660 


30 

0 

4 

3 

.3571 

i 

1 

4 

.4395 


45 

0 

4 

3 

.8326 

i 

1 

4 

.7165 

36 


0 

4 

4 

.3111 

i 

1 

4 

.9969 


15 

0 

4 

4 

.7914 

i 

1 

5 

.2808 


30 

0 

4 

5 

.2772 

i 

1 

5 

.6819 




















































80 


THE PRACTICAL MINERS’ 

SECOND TABLE.—PERPENDICULAR RADIUS. 


ANGLE. 

BASE. 

HYPOTHENUSE. 

Deg. 

Min. 

Fath. 

Feet 

Ins. 

Decimals. 

Fath. 

Feet, 

. Ins. 

Decimals. 

36 

45 

0 

4 

5 

.5650 

1 

1 

5 

.8591 

37 


0 

4 

6 

.2559 

1 

1 

6 

.1538 


15 

0 

4 

6 

.7501 

1 

1 

6 

.4520 


30 

0 

4 

7 

.2475 

1 

1 

6 

.7540 

38 

45 

0 

4 

7 

.7483 

1 

1 

7 

.0597 


0 

4 

8 

.2526 

1 

1 

7 

.3693 


15 

0 

4 

8 

.7602 

1 

1 

7 

.6831 


30 

0 

4 

9 

.2834 

1 

1 

8 

.0000 

39 

45 

0 

4 

9 

.7861 

1 

1 

8 

.3214 


0 

4 

10 

.3044 

1 

1 

8 

.6467 


15 

0 

4 

10 

.8265 

1 

1 

8 

.9761 


30 

0 

4 

11 

.3522 

1 

1 

9 

.3096 


45 

0 

4 

11 

.8818 

1 

1 

9 

.6473 

40 


0 

5 

0 

.4152 

1 

1 

9 

.9893 


15 

0 

5 

0 

.9525 

1 

1 

10 

.0956 


30 

0 

5 

1 

.4938 

1 

1 

10 

.6863 


45 

0 

5 

2 

.0392 

1 

1 

11 

.0413 

41 


0 

5 

2 

.5886 

1 

1 

11 

.4009 


15 

0 

5 

3 

.1420 

1 

1 

11 

.7651 


30 

0 

5 

3 

.7002 

1 

2 

0 

.1338 


45 

0 

5 

4 

.2624 

1 

2 

0 

.5049 

42 

15 

0 

5 

4 

.8291 

1 

2 

0 

.8855 


0 

5 

5 

.4002 

1 

2 

1 

.2686 


30 

0 

5 

5 

.9758 

1 

2 

1 

.6566 

43 

45 

0 

5 

6 

.5705 

1 

2 

2 

.0496 

15 

0 

5 

7 

.1411 

1 

2 

2 

.4476 


0 

5 

7 

.7308 

1 

2 

2 

.8507 


30 

0 

5 

8 

.3254 

1 

2 

3 

.2591 


45 

0 

5 

8 

.9250 

1 

2 

3 

.6727 

44 

15 

0 

5 

9 

.5296 

1 

2 

4 

.0918 


0 

5 

10 

.1393 

1 

2 

4 

.5163 


30 

0 

5 

10 

.7542 

1 

2 

4 

.9463 

45 

45 

0 

5 

11 

.3744 

1 

2 

5 

.3820 

15 

1 

0 

0 

.0000 

1 

2 

5 

.8234 


1 

0 

0 

.6311 

1 

2 

6 

.2706 


30 

1 

0 

1 

.2677 

1 

2 

6 

.7237 

1 

45 

1 

0 

1 

.9101 

1 

2 

7 

.1828 


































































OWN BOOK AND GUIDE. 

SECOND TABLE.—PERPENDICULAR RADIUS. 


81 


ANGLE. 

BASE. 

HYPOTHENUSE. 

Deg. 

Min. 

Fath. 

Feet. 

Ins. 

Decimals. 

Fath. 

Feet 

. Ins. 

Decimals. 

46 


1 

0 

2 

.5852 

1 

2 

7 

.6481 


15 

1 

0 

3 

.2122 

1 

2 

8 

.1195 


30 

1 

0 

3 

.8722 

1 

2 

8 

.5973 

47 

45 

1 

0 

4 

.5382 

1 

2 

9 

.0814 


1 

0 

5 

.2105 

1 

2 

9 

.5721 


15 

1 

0 

5 

.8892 

1 

2 

10 

.0694 


30 

1 

0 

6 

.5742 

1 

2 

10 

.5735 

48 

45 

1 

0 

7 

.2658 

1 

2 

11 

.0844 


1 

0 

7 

.9641 

1 

2 

11 

.6023 


15 

1 

0 

8 

.6692 

1 

3 

0 

.1273 


30 

1 

0 

9 

.3812 

1 

3 

0 

.6596 

49 

45 

1 

0 

10 

.1003 

1 

3 

1 

.1991 


1 

0 

10 

.8265 

1 

3 

1 

.7462 


15 

1 

0 

11 

.5601 

1 

3 

2 

.3009 


30 

1 

1 

0 

.3012 

1 

3 

2 

.8634 

50 

45 

1 

1 

1 

.0498 

1 

3 

3 

.4337 


1 

1 

1 

.8062 

1 

3 

4 

.0122 


15 

1 

1 

2 

.5699 

1 

3 

4 

.5987 


30 

1 

1 

3 

.3430 

1 

3 

5 

.1936 


45 

1 

1 

4 

.1236 

1 

3 

5 

.7970 

51 


1 

1 

4 

.9126 

1 

3 

6 

.4091 


15 

1 

1 

5 

.7101 

1 

3 

7 

.0300 


30 

1 

1 

6 

.5164 

1 

3 

7 

.6599 


45 

1 

1 

7 

.3316 

1 

3 

8 

.2990 

52 


1 

1 

8 

.1560 

1 

3 

8 

.9474 


15 

1 

1 

8 

.9893 

1 

3 

9 

.6053 


30 

1 

1 

9 

.8322 

1 

3 

10 

.2729 


45 

1 

1 

10 

.6848 

1 

3 

10 

.9505 

53 


1 

1 

11 

.5472 

1 

3 

11 

.6381 


15 

1 

2 

0 

.4197 

1 

4 

0 

.3360 


30 

1 

2 

1 

.3024 

1 

4 

1 

.0445 


45 

1 

2 

2 

.1956 

1 

4 

1 

.7636 

54 


1 

2 

3 

.0995 

1 

4 

2 

.4937 


15 

1 

2 

4 

.0143 

1 

4 

3 

.2350 


30 

1 

2 

4 

.9403 

1 

4 

3 

.9876 


45 

1 

2 

5 

.8776 

1 

4 

4 

.7520 

55 

II 

1 

2 

6 

.8267 

1 

4 

5 

.5282 

































































82 


THE PRACTICAL MINERS 


SECOND TABLE.—PERPENDICULAR RADIUS. 


ANGLE. 

BASE. 

HYPOTHENUSE. 

Deg. 

Min. 

Fath. 

Feet. 

Ins. 

Decimals. 

I Fath. 

Feet. 

Ins. 

Decimals. 

55 

15 

1 

2 

7 

.7876 

1 

4 

6 

.3165 | 


30 

1 

2 

8 

.7606 

1 

4 

7 

j .1172 1 


45 

1 

2 

9 

.7458 j 

1 

4 

7 

.9306 

56 


1 

2 

10 

.7444 

1 

4 

8 

.7570 


15 

1 

2 

11 

.7556 

1 

4 

9 

.6966 


30 

1 

3 

0 

.7801 

1 

4 

10 

.4497 


45 

1 

3 

1 

.8182 

1 

4 

11 

.3165 

57 


] 

3 

2 

.8703 

1 

5 

0 

.1976 


15 

1 

3 

3 

.9365 

1 

5 

1 

.0932 


30 

1 

3 

5 

.0174 

1 

5 

2 

.0034 


45 

1 

3 

6 

.1131 

1 

5 

2 

.9287 

58 


1 

3 

7 

.2241 

1 

5 

3 

.8697 


15 

1 

3 

8 

.3507 

1 

5 

4 

.8265 


30 

1 

3 

9 

.4933 

1 

5 

5 

.7994 


45 

1 

3 

10 

.6523 

1 

5 

6 

.7890 

59 


1 

3 

11 

.7281 

1 

5 

7 

.7955 


15 

1 

4 

1 

.0211 

1 

5 

8 

.8194 


30 

1 

4 

2 

.2317 

1 

5 

9 

.8612 


45 

1 

4 

3 

.4604 

1 

5 

10 

.9212 

60 


| 1 

4 

4 

.7077 

2 

0 

0 

.0000 





































OWN BOOK AND GUIDE. 


83 















84 


THE PRACTICAL MINERS 5 


THIRD TABLE. 
BASE RADIUS. 


ONE FATHOM. 


] ANGLE. 

hypothenuse. 

PERPENDICULAR. 

j Degrees. 

Fath 

Feet. 

Ins. 

Decimals. 

Fat&v 

. Fee 

t- Ins. 

DecimalsK 

1 

57 

1 

9 

.50554 

1 57 

1 

8 

1 .87726 

2 

28 

3 

11 

.06698 

28 

3 

9 

.81022 

3 

19 

0 

7 

.72726 

19 

0 

5 

.84186 

4 

14 

2 

0 

.16226 

14 

1 

9 

.64795 

5 

11 

2 

10 

.10734 

! Il 

2 

6 

.96374 

| * 

9 

3 

4 

.80760 

9 

3 

1 

.03424 

7 

8 

1 

2 

.79665 , 

! 8 

0 

10 

.39294 

8 

7 

1 

1 

.34135 

7 

0 

8 

.30662 

9 

6 

2 

4 

.25663 

6 

1 

10 

1 .59011 

10 

5 

4 

6 

.63148 

5 

4 

0 

.33229 

1 

5 

1 

5 

.34070 

5 

0 

10 

.40789 

12 

4 

4 

10 

.30087 

4 

4 

2 

.73337 

j 13 

4 

2 

8 

.06963 

4 

1 

11 

.86626 

14 

4 

0 

9 

.61672 

4 

0 

0 

.77622 

15 

3 

5 

2 

.18664 

3 

4 

4 

.70766 

! 16 

3 

3 

9 

.21278 

3 

2 

11 

.09384 

1 17 

3 

2 

6 

.26186 

3 

1 

7 

.50139 

j 18 

3 

1 

4 

.99690 

3 

0 

5 

.59321 

19 

3 

0 

5 

.15185 

2 

5 

5 

.10318 

20 

2 

5 

6 

.51392 

2 

4 

5 

.81837 

21 

2 

4 

8 

.91082 

2 

3 

7 

.56641 

22 

2 

4 

0 

.20164 

2 

2 

10 

.20626 

23 

2 

3 

4 

.26994 

2 

2 

1 

.62137 

24 

2 

2 

9 

.01872 

2 

1 

5 

.71465 

25 

2 

2 

2 

.36651 

2 

0 

10 

.40450 

26 

2 

1 

8 

.24438 

2 

0 

3 

.62187 

27 

2 

1 

2 

.59363 

1 

5 

9 

.30796 

28 

2 1 

0 

9 

.36392 

1 

5 

3 

.41231 

29 

2 I 

0 

4 

.51190 

1 | 

4 

9 

.89144 

































































OWN BOOK AND GUIDE. 


85 


THIRD TABLE.—BASE RADIUS. 


ANGLE. 

HYPOTHENUSE. 

PERPENDICULAR. 

Degrees. 

Fath. 

Feet. 

Ins. 

Decimals. 

Fath. 

Feet. 

Ins. 

Decimals. 

30 

2 

0 

0 

.00000 

1 

4 

4 

.70766 

31 

1 

5 

7 

.79549 

1 

3 

11 

.82812 

32 

1 

5 

3 

.86975 

1 

3 

7 

.22408 

33 

1 

5 

0 

.19765 

1 

3 

2 

.87028 

34 

1 

4 

8 

.75699 

1 

2 

10 

.74439 

35 

1 

4 

5 

.52817 

1 

2 

6 

.82666 

36 

1 

4 

2 

.49371 

1 

2 

3 

.09950 

37 

1 

3 

11 

.63809 

1 

1 

11 

.54722 

38 

i 

3 

8 

.94738 

1 

1 

8 

.15579 

39 

1 

3 

6 

.40913 

1 

1 

4 

.91260 

40 

1 1 

3 

4 

.01211 

1 

1 

1 

.80626 

41 

1 

3 

1 

.74622 

1 

0 

10 

.82652 

42 

1 

2 

11 

.60231 

1 

0 

7 

.96410 

43 

1 

2 

9 

.57201 

1 

0 

5 

.21055 

44 

1 

2 

7 

.64807 

1 

0 

2 

.55818 

45 

1 

2 

5 

.82338 

1 

0 

0 

.00000 

46 

1 

2 

4 

.09178 

0 

5 

9 

.52959 

47 

1 

2 

2 

.44758 

0 

5 

7 

.14108 

48 

1 

2 

0 

.88555 

0 

5 

4 

.82909 

49 

1 

1 

11 

.40094 

0 

5 

2 

.58864 

50 

1 

1 

9 

.98932 

0 

5 

0 

.41517 

51 

1 

1 

8 

.64669 

0 

4 

10 

.30445 

52 

1 

1 

7 

.36931 

0 

4 

8 

.25256 

53 

] 

1 

6 

.15377 

0 

4 

6 

.25589 

54 

1 

1 

4 

.99689 

0 

4 

4 

.31106 

55 

1 

1 

3 

.89577 

0 

4 

2 

.41494 

56 

1 

1 

2 

.84768 

0 

4 

0 

.56461 

57 

1 

1 

1 

.85016 

0 

3 

10 

.75735 

58 

1 

1 

0 

.90084 

0 

3 

8 

.99060 

59 

1 

0 

11 

.99760 

0 

3 

7 

.26196 

60 

1 

0 

1 11 

.13844 

0 

3 

5 

.56922 


4 
































THE PRACTICAL MINERS’ 




LEVELING. 

Rule.— Add all the perpendiculars to¬ 
gether for the base line or horizontal 
distance, and subtract the bases made by 
the angles of elevation and depression, one 
from the other for the perpendicular or 
difference of height.* 

EXAMPLE. 

Being required to level an irregular piece 
of ground, I measured in a S. W. direction 
64 yards from A to B, on an angle of 
depression 9° 4from this station, I 
measured 120 yards from B to C, in the 
same cardinal direction, on an angle of 
elevation 16° 30', and from thence to the 
extent of the ground—the line on the same 
course measured 44 yards from C to D, 
and the angle of depression 7°—required 
the base line or horizontal distance from 
the place where the leveling was begun, to 
the point where it was ended, also, how 
much higher or lower the ground is at the 
place where the operation terminated, than 
where it commenced ? 


!//, * The altitudes of irregular hills are generally 

ascertained by the assistance of a spirit level and 
perpendicular poles, and if the ground rise and 
descend alternatively, the difference between the 
heights of the poles are added when ascending, 
and subtracted when descending. In order to 
determine the different elevations and depressions 
of the ground, the foregoing rule and method will 
be found far more correct and masterly, remem¬ 
bering, always, that the height of the instrument 
be accounted for, which may easily be done by 
taking the observation from a staff or target the 
same height as the instrument. 














OWN BOOK AND GUIDE. 


87 


PERPENDICULARS. 

ft. in. fath. ft. 

in. 

Z 90 45'=5 

10 

.96004 X 32=189 

2.72128 

Z16° 30'=5 

9 

.03502 X 60=345 

2.10120 

Z 7° O'—5 

11 

.46333 X 22=131 

0.19326 


3)665 5.01574 


A E.—221 yds. 2 ft. 5 in. 


BASES. 


ft. 


fZ 9° 45'=1 

| £ 70 o'—0 

Depression. ^ 


( 

f /16° 30'= 1 


Elevation. 


I 


. ) Horizontal distance 

Ans * \ Elevation ED. 


in. fath. ft. in. 

0.19316 X 32= 32 6.18112 
8.77459 X 22 = 18 1.04098 


50 

7.22210 

8.44910 X 60=102 

2.94600 

3) 51 

7.72390 

17 yds. 

, 0 ft. in. 

yds. 

ft. in. 

A E.221 

2 5 

. 17 

0 



Suppose it were required to find the difference of level 
between the points A and G —a staffis erected at A; the in¬ 
strument is set up at B; another staff at C, at the same distance 
from B that B is from A. The readings of the two staves 
are then noted; the horizontal lines connecting the staves 
with the instrument represent the visual ray or line of sight. 
The instrument then is conveyed to D, and the staff which 
stood at A is now removed to E, the staff C retaining its former 
position, and from being the forward staff at the last observa- 





















88 THE PRACTICAL MINERS' 

tion, it is now the back staff—the readings of the two staves 
are again noted, and the instrument removed to F, and the 
stafi C to the point G; the staff at E, retaining the same posi¬ 
tion, now becomes, in its turn, the back staff, and so on to 
the end of the work, which may thus be extended many 
miles—the difference of any two of the readings will show 
the difference of level between the places of the back and 
forward staff; and the difference between the sum of the back 
sights and the sum of the forward sights, will give the differ¬ 
ence of level between the extreme points, thus: 

Back Sights. Fore Sights. 


ft - dec. ft. dec. 

A and C.10 .46 11 .20 

C and E.11 .33 8 .00 

E and G. 7 .42 7 .91 


Sum. 29 .21 27 .11 


27 .11 


Difference of level.... 2 .10 










OWN BOOK AND GUIDE 


89 


HORIZONTAL 

OR 

TRAVERSE SURVEYING. 


Plain sailing in navigation, and horizontal surveying in 
mining, are nothing more than the practice of right-angled 
trigonometry, calling the hypothenuse the distance, the per¬ 
pendicular the difference of latitude, the base the departure, 
and^the angle opposite the base the course; consequently any 
range of surveying, however complicated and extensive, may be 
reduced into a single triangle, the perpendicular of which will 
either be the east and west, or north and south line, according 
to the main direction or bearing of the work, the hypothenuse 
will be the actual length of the surveying, in a right line from 
the point of setting out to the termination, the base will be 
the distance the terminating point will fall right or left of the 
perpendicular, and the angle by the hypothenuse with the per¬ 
pendicular will be the final course or direction of the work. 

It therefore follows, that the general practice of repeating or 
retracing a course of underground surveying on the surface 
may be avoided, and thereby the difficulties and dangers arising 
from obstructions, irregular ground and the attraction of the 
magnet by iron, which always abounds in the vicinity of a mine, 
be done away. What is said of Mercator’s sailing may, in the 
chief respect, be applied to horizontal surveying, viz : It is the 
art of finding on a plane Surface the motion of a ship upon any 
assigned course by the compass, which shall be true in latitude, 
longitude, and distance sailed; and certainly this includes the 



90 


THE PRACTICAL MINERS’ 


whole theory and practice of navigation,and ifany method could 
be devised for measuring a ship’s course and distance truly, 
nothing would be wanting; also, in surveying, it is only requir¬ 
ed to find a method for reducing the various windings and an¬ 
gles of a level or adit into a right line, and discovering the 
real extent and direction of that line, to complete the art. 

But not to occupy the readers time in telling him what he 
well knows already, we shall proceed to introduce the pro¬ 
cess for obtaining the length and bearing of a course of traversed 
surveying by the trigonometrical tables. The first thing to 
be attended to is the statement of the work, or so placing the 
drafts that there may be no confusion in the operation, and 
that the perpendiculars and bases may fall on their proper 
sides. In order to succeed in this essential matter, which 
may be considered the foundation of the work, note on which 
cardinal point the main direction of your surveying runs, 
whether east, west, north or south, and reckon off your de¬ 
grees, right or left, from that line, thus : if your surveying 
runs easterly or westerly, let the equator or east and west 
line be the point for numbering off your angles; if northerly 
or southerly, the meredian or north and south line, conse¬ 
quently this line will be the perpendicular of every triangle in 
the operation that comes within the sweep of half the circle 
or 180°; and should any of the drafts return beyond the 
north or south points, or exceed 90° right or left of the east 
point, then the angle must be counted from the west toward 
the north or south, as the draft may happen to incline. This 
being done, it is evident that on a course of east and west 
surveying, the bases north and the bases south must be sub¬ 
tracted one from the other, and the remainder will be the 
departure or base line, north or south as the surveying may 
have prevailed on this or that side, and if any of the drafts 
have gone westerly, then the perpendiculars west must be sub¬ 
tracted from the perpendiculars east, for the real length of the 
perpendicular, but if the surveying has prevailed most in a 


OWN BOOK AND GUIDE. 


91 

westerly direction, the perpendicular will lie on that side; in 
short, as a matter of course, either for the difference of latitude 
or rather difference of longitude in this case, (the perpendicu¬ 
lar,) or for the departure, (the base,) the lesser number must 
be taken from the greater, and the difference will show the 
sides on which the operation lies. This process must all be 
performed by the first table, where the hypothenuse is given, 
because in every case the actual measured line will be the 
longest side of the triangle and after stating the work, as before 
directed, take out the numbers standing against the given an¬ 
gles in the table, and multiply them respectively by the length 
of the hypothenuse, reduced into fathoms and parts, (if any,) 
and place them in their proper positions until the whole has 
been calculated, then take the sum of the bases north and 
south, one from the other, and the sum of the perpendiculars 
east and west, one from the other, the perpendicular remain¬ 
ders will show the east and west line, and the bases the dis¬ 
tance the surveying has extended north or south of that line. 
The work is now brought to that case where the difference of 
latitude and departure are given to find the course and distance, 
and in order to avoid the necessity of introducing extensive 
and intricate tables, used by navigators for this purpose, we 
shall have recource to one simple act of instrumental opera¬ 
tion, and as two sides of the triangle are given, the thing may 
be quickly and safely performed; thus, draw the base the 
given length by a scale of equal parts, raise the perpendicular 
on one end of the base, (and of course at right angle therewith) 
and mark off the given length, draw the hypothenuse, and the 
triangle will be complete, then, by the same scale, measure 
the hypothenuse and it will be the actual length of the survey¬ 
ing in a right line, from beginning to end, then, with a pro¬ 
tractor or scale of chords, measure the angle opposite the de¬ 
parture or base, and it will be the true course, bearing or di¬ 
rection of the extreme points. The degrees on the miner’s 
compass are generally graduated from 1 to 360, and are fi- 


92 


THE PRACTICAL MINERS’ 


gured toward the left hand, consequently 90° stands at the 
west point, 180° at south, 270° at east, and ends with 360° 
at the north; and where the same course is to be pursued, 
that is, when the angles are to be taken and the drafts mea¬ 
sured again, there will be no necessity for finding the real di¬ 
rection of the line, for as the sights are always fixed, the sur¬ 
veyor need only to be careful to observe that the needle stands 
at the same degree as in the original course, but when the 
operation is to be plotted or trigonometrically proved, there 
will be a necessity for ascertaining the actual bearing of every 
draft in the work, and this may be done by the following 
rule. 

RULE. 


(Sights fixed north and south.) 


i Cl 
a> o 

a rn 


f From 1 to 90 N.to W.'l J jg g . f E. of N. comp. N. of E. 
J From 90 to 180 W. to S. 1 |.g>| I S. of E. comp. E. of S. 
■ From 180 to 270 S. to E. j ‘<5 ® j W. of S. comp. S. of W. 
(^From 270 to 360 E. to N. j |j £ 7 £ a f N. of W. comp. W. of N. 




OWN BOOK AND GUIDE 


93 


i 

\ 


\ 

V 

\ 
















94 


THE PRACTICAL MINERS’ 


EXAMPLE 1. 

It is required to sink a perpendicular shaft on the end of a 
level whose angles and drafts measured as follows, viz : 






ft. 

in. 


fath. 

ft. 

in. 

Z16° 

30' 

E. 

of S. 

53 

6 

or 

8 

5 

6 

/26° 

O' 

W. 

, of S. 

22 

11 

or 

3 

4 

11 

Z19° 

0' 

E. 

of S. 

58 

0 

or 

9 

4 

0 

o 

CO 

Vi 

30' 

W. 

, of S. 

21 

6 

or 

3 

3 

6 

Z57° 

o 

CO 

,w. 

, of S. 

53 

8 

or 

8 

5 

8 

Z39° 

30' 

E. 

of S. 

29 

10 

or 

4 

5 

10 


What distance is the end C, (in the annexed plate,) where 
the surveying was finished, from the engine shaft A, where the 
surveying was begun, and what is the bearing of the line A C, 
or how many degrees are contained in the angle B A C ? 

OPERATION. 

Bases. 

ft - in- fath. ft. in ft. in. 

E. of S. 164°=1 8.44910 X 8 5 6=15 2.33790 

! W.ofS. 26° =2 7.56272 X 3 4 11 = 10 0.-53916 

E. of S. 19° =1 11.44091 x 9 4 0=18 10 58864 

W. of S. 34£°=3 4.78125 X 3 3 6=12 2.13235 

W.ofS.574°=5 0.72418 X 8 5 8=45 3.18762 
E. of S. 39£°=3 9.79763 X 4 5 10=18 11.55815 


ft. in. 

Sum of bases W. of S.67 5.85913 

Sum of bases E. of S.53 0.48469 


Base or departure westerly, B C=14 5.37444 







Scale 40 feet to an inch. 


OWN BOOK AND GUIDE 


95 



* 













96 


THE PRACTICAL MINERS’ 


Perpendiculars. 


ft- in. fath. ft. in. ft. 

/16i°=5 9.03502 X 8 5 6=51 3.56228 

/26 °=5 4.71317 X 3 4 11=20 7.16851 

Z19 °=5 8.07734 X 9 4 0=54 10.06606 

34i°=4 11.33709 X 3 3 6=17 8.62417 

57^=3 2.68557 X 8 5 8=28 10.05018 

39£°=4 7.55697 X 4 5 10=23 0.04485 


Perpendicular or difference of latitude, A B 196 3.51605 


Then , by construction. 

Draw two lines at right angles, as A B and B C, and of an 
indefinite length, take 196 feet, 3^ inches in your compasses, 
from a scale of equal parts, and with one foot in the right 
angle B, point off the distance B A for the perpendicular. 
Again, take 14 feet, inches, from the same scale, and apply 
it to the other line B C for the base; draw the hypothenuse 
to join A C, which by the same scale will be found to measure 
197 feet. 

For the Jingle. 

With the chord of 60° in your compasses and centre 
A, describe an arc, e d, cutting A B and A C in d and e; then 
take the distance e d in your compasses, and setting one foot 
on the brass-pin at the beginning of the chords on your scale, 
observe how many degrees the other foot reaches to, which 
will be 4° 15' for the arc e d or angle B A C. 

Answer. 197 feet, on an angle of 4° 15' west of south. 


EXAMPLE 2. 


Given 


the following course of traverse surveying, 


<D <D 


eg 


162 °=/18° O' S. of E. 
143^-/36° 15' S. of E. 
16£°=/ 73° 30' N. of E. 
257i°=/12°45' S. ofE. 

45 °=/45° 0'N. of E. 

7i 0 -/82° 15'N. of W. 15 
152 i°“ Z27° 30' S. ofE. 72 
87*°-/ 2° 30' N. of E. 16 
204*°=/65° 30' S. of W. 73 


viz 

in. fath. ft. 

0 or 6 0 


4 or 
9 or 
6 or 
17 10 or 
3 or 


7 2 
5 0 
4 4 
2 5 
2 3 
0 or 12 0 


0 or 
0 or 


2 4 

12 1 


0 

4 

9 

6 

10 

3 

0 

0 

0 





OWN BOOK AND GUIDE. 


97 


Required the distance and bearing of the extreme points 
A C? 

OPERATION. 

Base Southerly, 
ft. in. fath. ft. 

180 O'—1 10.24922 X 6 0 
360 15'= 3 6.57429 X 7 2 

12 o 45 /= i 3.89021 X 4 4 

27° 30'=2 9.24590 X 12 0 0= 

65° 30'=5 5.51721 x 12 1 


ft. 

73° 30'=5 
450 O '—4 
82° 1 5'=5 
2° 30 /= =0 


Bases Northerly, 
fath. ft. 

0 

5 : 

3 

4 


in. 

9.03502 X 5 
2.91169 X 2 
11.34234 X 2 
3.14060 X 2 


Perpendiculars Easterly. 


ft. in. fath. ft. 

18° 0'=5 8.47607 X 6 0 

360 15'=4 10.06401 X 7 2 
73° 30 /= =l 8.44910 X 5 0 

12° 45^5 10.22464 x 4 4 
450 o'—4 2.91169 x 2 5 

27° 30 /= =5 3.86478 X 12 0 

2° 30'—5 11.93147 X 2 4 


in. 


1. ft. 


)—11 

1.49522 

1=26 

2.57669 

’>= 6 

3.44849 

1—33 

2.95080 

1—66 

5.12605 

143 

3.59725 

t. ft. 

in. 

'==29 

5.80448 

1—12 

7.14507 

1=15 

1.33685 

1 = 0 

8.37150 

57 

10.65790 

ft. 

in. 

=143 

359725 

= 57 

10.65790 

. 85 

4.93935 

ft. 

in. 

=34 

2.85642 

=35 

9.02851 

= 8 10.80163 

=27 

9.56704 

= 12 

7.14507 

=63 10.37736 

= 15 11.81724 


399 1.59327 
















98 


THE PRACTICAL MINERS’ 


Perpendiculars Westerly, 
ft. in. fath. ft. in. ft. in. 

82° 15'—0 9.70926 X 2 3 2= 2 0.67815 

65° 30'—2 5.85791 X 12 1 0—30 3.27124 


32 3.94939 


From perpendiculars east.—199 1.59327 

Subtract perpendiculars west.== 32 3.04939 


A B 166 9.64388 


ft. in. 

Perpendicular or east and west line, A B. ... 166 9.64388 

Base south of east, C B. 85 4.93935 

Then by construction (as before) the hypothenuse A C will 
be found 187 feet 3 inches, and the angle p q 27 degrees 
south of east. 











OWN BOOK AND GUIDE. 


99 


THE 

PRACTICAL MINERS’ GUIDE. 

PART IX. 

INTRODUCTION. 

The qualifications necessary to constitute an accomplished 
miner are more numerous and difficult of attainment than is 
generally imagined, even by persons deeply interested in 
mining affairs ; and although it may not be expected that every 
one who fills a mining situation should be an adept in ail 
the various branches of the art, yet it is certainly highly 
desirable and necessary that agents, who have the manage¬ 
ment of large concerns, should possess a general knowledge 
of everything connected with the profession of a miner, 
especially of surveying and ventilation, as it is a melancholy 
fact, that nearly all the lives that are lost in all countries in 
mining operations are the results of bad and inefficient ventila¬ 
tion, or from tapping old workings filled with water unexpect- 
edly, by having inaccurate plans of the underground workings 
or of not being able to read or understand the scale on the 
plan, and although there are government inspectors appointed 
in England, accidents are of almost every day occurrences, 
either from explosions or from tapping the water in old work¬ 
ings, unexpectedly, resulting in serious loss of life and in¬ 
calculable loss of property. In the year 1815 an inundation 
took place at Heaton Colliery, whereby ninety lives were lost. 
The water of the old Heaton and Jessamand Collieries, which 
had been abandoned for several years, was let in, owing to 
working too near, and all for the want of a correct plan, show¬ 
ing the extent of the old workings. In the year 1837 an 
inundation took place in England, at Workington Colliery, 
by which thirty-six men and boys were lost, and several 


1U0 THE practical miners’ 

valuable horses, none of whom have ever been found nor 
never will be. In the year 1843 an inundation took place at 
a colliery called Landshipping, in the county of Pembroke, in 
England, by which forty men and boys lost their lives. In 
the year 1856 the water in the old workings, that had been 
abandoned for several years, was unexpectedly tapped at the 
Midlothian Colliery, in Chesterfield county, Virginia, from 
having an inaccurate plan of the old workings, which resulted 
in the loss of several lives and a great loss of property; and 
if the accident had taken place in the day time instead of night, 
the loss of life would have been greatly increased—and within 
a few months, we have accounts of similar and equally as 
lamentable catastrophes happening, and which are now looked 
upon as mere matters of course. There are other subjects 
essential also to the practical miner who expects to have the 
management of other mines besides coal mines, and require 
no comment to set forth their utility. They may also be 
found useful and interesting to persons not immediately 
engaged in mining pursuits. The first article consists in a 
description of the art of assaying silver, and as this has, almost 
up to the present time, been a secret in the possession of but 
few persons, it cannot but be expected that this will form an 
acceptable part of this work. The next part of this work 
contains a plain statement of the method of assaying copper, 
including the established process of one of the most experi¬ 
enced and respectable copper assayers in the old world. 
Rules for assaying lead and tin follow in succession, and this 
part of the treatise concludes with a description of the manner 
of extracting silver from copper ore, or of discovering the 
quantity of silver the copper ore contains, and probably this 
may be productive of beneficial effects to the mining interest 
of this country, as there is great reason to believe that a 
considerable quantity of silver is contained in the ores pro¬ 
duced from many of the American copper mines of Lake 
Superior, North Carolina, and other places. The method is 
very simple and the trial may be quickly and satisfactorily 
made. 


OWN BOOK AND GUIDE. 


101 


ASSAY OF SILVER ORE. 

Sample. —One ounce avoirdupois, pulverized and sifted 
through a line hair sieve, then well mixed in the scoop with 
the following flux, viz : 

Red lead*. . . 2 G z 

Red tartar . dwts. 

N,tre .9 dwts. 

Borax . dwts. 

L,me . . oz. 

.2 oz. 

Fluor spar (bruised)... i oz 

Smelt the ore in a wrought iron crucible, if this cannot be 
conveniently procured, and a stone pot used, add 1 oz. of 
iron. The sample will melt in a good heat in about twelve 
minutes if the ore is tolerably free from sulphur and iron, 
otherwise it will require more time. When the sample has 
become quite fluid, take it out and pour it in a mould prepar¬ 
ed to receive it, having been anointed on the inside with grease 
or oil; the process of taking out and pouring the sample must 
be done quickly, otherwise a degree of chill will take place so 
that the metal will not run freely out of the crucible and the 
assay will in consequence be imperfect. If the operation has 
been properly managed, the lump will separate clean from the' 
slag or dross by a slight blow, but if the metal and dross stick 
together the assay is impure; it is probable a little more nitre 
would remedy this defect. Should the lump when broken 
display the metal disseminated throughout and uncombined 
among the slag it is a proof the sample was not sufficiently 


*An ounce of red lead generally contains about one-thirty second 

part of a grain of silver, or nearly three ounces of silver in a ton._ 

The proportion of silver contained in the flux must first he known and 
the regular deduction made from the produce in order to obtain a true 
assay. 


5 










102 


THE PRACTICAL MINERS’ 


flowed or not kept time enough in the furnace. If the heat 
is too strong or the sample left too long a time in the fire it 
will set or become dry and callous, and this change will take 
place to all appearance quite suddenly. Either the former 
circumstance of too low a heat or this of too high, renders the 
assay irremediable. Should the sample appear stubborn and 
refuse to melt in a brisk heat, add more nitre. 

Testing or Refining Process. 

The test or cupel should be composed of four-fifths bone 
ashes to one-fifth fern ashes, damped and well beat into an 
iron ring two and a half inches deep and six inches in circum¬ 
ference. The test should be put in the fire an hour or more 
before the refining process is begun, otherwise the silver will 
be apt to be agitated by the unsettled test, spring over and 
consequently the assay be destroyed. Should the assay set in 
refining before it has become pure throw in about half an 
ounce of potter’s lead.* 

If the fire is permitted to get low or too much air admitted 
into the furnace the assay will be apt to turn to litharge; 
whenever this happens increase the fire by putting in a few 
pieces of bituminous coal instead of coke, at the same time 
sprinkle a little coal-dust on the test. When the assay is 
thoroughly pure or fine it will assume a globular shape, set, 
or become fixed, and in a few moments will throw up sprouts 
or branches from the top. Take out the test, weigh the pril- 
lion, find in the table the produce or value per ton, and the 
work will be complete. 

ASSAY OF COPPER ORE. 

Sample.— Four hundred grains, pounded well in a morter 
and sifted through a fine hair sieve, : put in an earthen crucible 
and frequently stirred while in the furnace with an iron rod , 

*The fire should be gradually increased toward the close of the pro¬ 
cess. A muffle or arched cover to the test would prevent the air from 
taking an unfavorable effect on the assay, while the furnace is opened 
for the purpose of increasing the fire by adding coal, wood or coke. 





103 


OWN BOOK AND GUIDE. 


or paddle—the sulphur will be seen to go off in white fumes- 
the process must be continued until this evaporation ceases’, 
or nearly so, winch will generally occupy from one to two 
hours. Great attention must be paid during this operation, in 
order that a standard regal may be obtained, which being 
one, there will be no danger of producing a true assay. The 
oi(i, during the process, must be kept in a free, sandy state, 
which will be effected by stirring, and constant regulation of 
the degree of heat. If the ore becomes moist and begins to 
stick or adhere to the crucible, it must be immediately taken 
out of the fire, and stirred a short time till this effect has 
ceased, and then returned. When it has become tolerably 
free of sulphur, it may be discovered by the evaporation 
having nearly ceased*—this being observed, take it out of the 
fire and let it gradually cool in the crucible; and if, when cold, 
the upper part appears red or brown, and the under part black, 
it is a proof of its having been well calcined. This being 
done, add standard flux, viz: ' 


Borax. 

Lime. 


.5 dwts. 


...1| ladle.f 

Fluor spar (pulverised).I j a( ]j e> 

Mix these together with the calcined ore in the crucible, and 
cover the whole with salt—let it melt well and a regal will be 
produced. 


Marks and Remarks. 


A good or standard regal is brown, and full of cracks or 
fissures, and of a spherical shape. Should it come out flat, it 
is a mark of its not having been well calcined, and may be 
thrown back again with a small quantity of nitre. Should a 
regal come out too low or coarse, (having, when broken, a 
cimiter-like, or cellular appearance,) throw it back with addi¬ 
tional nitre; if too high or fine, (having, when broken, a 

* It is only some very stubborn ores, containing a mixture of metals, 
or semi-metals, which require to be so effectually roasted or calcined! 
f Common assaying ladle—diameter f inch, depth | inch. 






104 


THE PRACTICAL MINERS’ 


metalic appearance,) return it to the crucible with a ladle of 
sulphur, in either case let it work well together a short time, 
and, in all probability, a standard regal will be produced. A 
regal may be considered good, which will produce from eight 
to twelve in twenty, and this quality is easily known by in¬ 
spection, but if less than eight, or above twelve, it would be 
better to reject it and begin the process again with a new 
sample. Grey, black and green ores require a proportion of 
sulphur, in order to throw them back, as they contain too 
little of this mineral in their composition to produce a good 
assay. Should a regal be too fine, put less nitre with it in 
refining, and, therefore, the coarser it is, the more nitre will 
be required. 

Fining Process. 

Pound or pulverise the regal, put it in an earthen fining pot, 
and re-calcine it until perfectly sweet, (i. e., free from sulphur,) 
which may be discovered, both by the appearance and fumi¬ 
gation, then add 

3 dwts.) 

^5 dwts* ' Covered or sprinkled with salt. 

2 ladles.' J 

This brings down the assay into coarse copper. Should it 
come out having a transparent or horn-like appearance, add 
four dwts. of nitre and a ladle of salt, letting it work well in 
the fire. Should the assay come out black, plate it, and if the 
black flies off in flakes or scales, it is a proof of its not having 
been sufficiently calcined; if not, its color may be attributed 
to lead or a mixture of metals, the former defect renders the 
assay hopeless. Should it come out clean, put the assay in 
the pot without flux, and when fluid, take out the pot and 
shake it gently until the surface assumes an azure or blue 
appearance, then put— 


Nitre 
Red tartar, 
Borax. .. 
Salt. 






OWN BOOK AND GUIDE. 105 

Refining flux,* (viz: two parts nitre to one part white 

sulphur,). 5 dwts. 

Salt ... -. 1 ladle. 


Preparatory to pouring into the crucible, place the refining 
flux in the mouth or fore part of the scoop, and the salt behind; 
throw it in with the assay and let it melt until the flux settles 
well down, then pour the copper into one mould, and the 
slag or scoria into another; return the slag into the same pot 
with two ladles of red tartar, and let it melt well down; take 
out the prillion and weigh it with the lump for the produce, 
and the work will be completed. 

ASSAY OF LEAD ORE. 

Sample.— One ounce avoirdupois. 

Flux. 


1 common ladle.red tartar. 

1 ditto .spar. 

2 ditto .salt. 

h ditto .borax. 

4 ditto .nitre. 

\ ditto .lime. 


Mix the flux with the sample and put in an iron crucible, 
stir it with an iron rod during the latter part of the process; 
in about five minutes in a brisk heat the sample will be down, 
provided the crucible was red hot when the assay was thrown 
in, which should always be the case. If the sample to be tried 
weighs four ounces, the proportionate quantity of flux must 
be added agreeably with the above statement. It may be dis¬ 
covered when the sample is ready by the grating of the rod 

* The refining flux should go through a calcining process before it 
is used; it may be done by putting two parts nitre to one part white 
tartar, in an iron mortar, to which apply a red hot iron, and stir it 
therewith until the deflagration has ceased; when cold, powder and 
sift it. This operation will prevent any commotion during the re¬ 
fining, which otherwise may be so violent as to cause some of the 
metal to spring out of the crucible, and thereby the assay be spoiled. 













106 


THE PRACTICAL MINERS’ 


against the bottom of the crucible in stirring, it should then be 
immediately taken out and poured. The metal will separate 
clean from the slag in a good assay. To assay lead ore for 
discovering the quantity or proportion of silver it contains, the 
foregoing method must first be used and the assay then test¬ 
ed precisely the same way as described for refining a silver 
sample, page 101. The lead will go off in vapour, and the 
silver remain in the test. 

ASSAY OF TIN ORE. 

Sample.— Two ounces black tin. 

Flux. 

.£ weight of sample. 

.4 dwts. 


Culm. 

Borax 


Process. 

If the ore contains a large proportion of iron, add more 
culm ;* when the sample is properly down or flowed, the sur¬ 
face of the assay in the crucible will be perfectly smooth and 
motionless, in a strong heat this will occur in about twelve 
minutes. When taken out of the fire stir it well with an iron 
rod before you pour it, afterwards scrape the crucible, pulver¬ 
ise the scrapings in a mortar and then van or wash them on a 
shovel. The prillion of a standard sample will not exeed two 
in twenty. The criterion for the lump is its possessing a 
maleable quality or bending to the hammer without breaking. 
Grain tin may be treated in every respect as the above, except 
in the subsequent addition of culm which will not be required. 


*If the sample is very stubborn add a small quantity of pulverised 
fluor with the culm. 






OWN BOOK AND GUIDE. 


107 


METHOD OF DISCOVERING THE PROPORTION OF 
SILVER CONTAINED IN COPPER ORE. 
Sample.— One ounce. 


ladle. 


ditto. 


ditto. 


ditto. 


ditto. 


ditto. 



Well mixed with the ore and melted in a wrought iron cruci¬ 
ble,* about eight minutes in a brisk heat will be sufficient, the 
last five minutes the assay should be incessantly stirred with 
an yon rod, pour the sample and cool it, then break out the 
lump and test it in the usual way. 


Remarks. 

Soon as the assay begins to flow, the lead by the power of 
affinity will presently attract the silver, or the silver, by the 
same law, will attach itself to the lead, and this being effected 
it only requires the process of refining or burning off the in¬ 
ferior metals to find the produce. 


*If a stone crucible be used, one ounce of iron must be added to 
the flux. 










108 


TIIE PRACTICAL MINERS’ 


A TABLE 

Showing the number of ounces and parts o f an ounce of silver 
contained in a ton of ore , by assay , produced 
from one ounce avoirdupois. 


Assa 

r Per Ton. 

Assa 

y Per Ton. 

II 

11 

Assa: 

r 1 Per Ton. 

grs. 

oz. 

dwt 

• grs 

grs. 

j oz. 

Idwt 

. grs 

•j| grs. 

1 oz. 

jdwt. 

' grs. 

| 

fV 

$ 

2 ( 

16 

4 

1 29£ 

$ 13 

: s 

i|| 8J 

606 

13 

8 

tV 

i 

l 1c 

8 

i 

8 

■l| 30S 

s C 

> c 

> i 

1 616 

0 

0 

i 

c 

6 

16 

1 

4 

1 317 

H 6 

» ! 16 # 

i 625 

6 

i 16 

i 

4 

IS 

13 

8 

1 

| 326 

i ! 13 

: fi 

! i! i 

634 

1 13 

i 8 

f 

2§ 

0 

0 

F 

! 336 

i 0 

0 

'll | 

644 

0 

o 


3? 

6 

16 

8 

j 345 

; 6 

| 16 

'j £ 

653 

6 

16 

I 

46 

13 

8 

3 

j| 354 

I 13 

1 8 

$ 

662 

13 

8 

i 

56 

0 

0 

i 

364 

0 

1 0 

1 9 

1 672 

0 

6 

0 

16 

i 

65 

6 

16 

5 

373 

6 

16 

j i 

681 

1 

74 

13 

8 

i 

8 

382 

13 

8 

i ® 

i 

690 

!3j 

1 8 

i 

8 

84 

0 

0 

F 

392 

0 

0 

3 

1 tf 

1 700 

1 0 

0 

F 

1 

93 

102 

6 

13 

16 

8 

h 

401 
| 410 

6 

13 

16 

8 

i 

i 2 
& 

8 

709) 

7181 

6 

13 

16 

8 

i 

112 

0 

0 

1 

420 

0 

0 

£ 

728 

o 

0 

| 

121 

6 

16 

1 

4291 

6 

161 

i 

737 

6 

16 

* 

130 

13 

8 

i 

438 

13 

81 

10 

746 

13 

8 


140 

0 

0 

6 

*448 

0 

0| 

A 

756 

0 

0 

2 

149 

6 

16 

JL 

8 

457 

6 

16! 

1 8 

1 

765 

6 

16 

i 

158 

13 

8 

k 

466 

13 

8 

1 ^ 

774 

13 

8 


168 

0 

0 

1 

476 

0 

o! 

1 

784 

0 

0 

1 

177 

6 

16 

2 j 

485 

6 

16 

1 j 

1 

793 

6 

16 

i 

186 

13 

8 

t 

1 494 

13 

8 

J 

802 

13 

8 

t 

196 

0 

0 

£ 

I 504 

0 

0 

7. 

8121 

0 

o 

1 

205 

6 

16 

i\\ 

1 513 

6 

16 

11 

821 

6 1 

16 

1 

3 

214 

224 

13 

0 

8 

0 

7 

i 

8 

522 

532 

13 

0 

8 

0 

i i 
F I 

1 l! 

830 

840 

13 ! 
o 

8 

0 

F 

233 

6 

16 

£ 1 

541 

6 

16 

*+ 1 

849 

6 

16 

i 

1 

242 

252 

13 

0 

8 

0 

! 

550 

560 

13 

0 

8 

0 

f l! 

2 | 

|! 

8.-58 

868 

13 1 

0 

8 

0 


261 

6 

16 1 

| 

569 

6 

16 


877 

6| 

16 

f 

270 

13 

8 


578 

13 

8 

i ! 

886 

13 1 

8 ! 

! 

280 

2891 

0 

6 

0 

16 II 

I 

8 

588 

597 

0 

6 

0 

16 1 

O ! 

12 

i ii 

8 !| 

896 
905 1 

0 

6i 

0 i 

16 1 




































































































OWN BOOK AND GUIDE. 109 


SILVER ASSAY TABLE.— Continued. 


Assay 

Per Ton. 

Assay 

Per Ton. 

Assay 

Per Ton. 

grs. 

oz. 

dwt 

grs. 

grs. 

U°z. 

dwt, 

. grs. 

grs. 

oz. 

| dwt. 

grs. 

12* 

914 

13 

8 

I m 

1260 

0 

1 0 

21J 

1605 

; 6 

16 

| 

924 

0 

0 

17 

1269 

6 

• 16 

f 

1614 

13 

8 

i 

933 

6 

16 

A 

8 

1278 

13 

: 8 

3 

1624 

: 0 

0 

t 


13 

8 

0 

i 

1288 

0 

0 

¥ 

1633 

6 

16 

1 

952 

0 

| 

1297 

6 

16 

22 

j 1642 

13 

8 

¥ 

961 

6 

16 

h 

1306 

13 

8 

A 

O 

1652 

0 

0 

13 

970 

13 

8 

5 

¥ 

1316 

0 

0 

O 

i 

1661 

6 

16 

i 

8 

980 

0 

0 


1325 

6 

16 l 


1670 

13 

8 

1 

4 

989 

6 

16 

1 

1334 

13 

8 

i 

1680 

0 

0 

f 

998 

13 

8 

18 

1344 

0 

ol 


1689 

6 

16 

1 

2 

1008 

0 

0 

1 

1353 

6 

16 

J 

1698 

13 

8 

»i 

1017 

6 

16 

4 

1362 

13 

8 


1708 

0 

0 

3 

¥ 

1026 

13 

8' 


1372 

0 

0 

23 

1717 

6 

16 

1 

1036 

0 

0! 

1 

2 1 

1381 

6 

16 

i 

8 

1 

4 

1726 

13 

8 

14 

1045 

6 

16! 

5 

1390 

13 

8 

1736 

0 

0 

¥ 

1054 

13 

8 

4 

1400 

0 

0 

1745 

6 

16 

i 

1064 

0 

0 

7 

¥ 

1409 

6 

16 

l 

1754 

13 

8 

1 

1073 

6 

16 

19 | 

1418 

13 

8 

f 

1764 

0 

0 

¥ 

1082 

13 

8 

i 

¥ 

1428 

0 

0 


1773 

6 

16 

¥ 

1092 

0 

0 

1 

4 

1437 

6 

16 

i\ 

1782: 

13 

8 

* 

1101 

6 

16 ! 


1446 

13 

8 

24 

1792 

0 

0 


1110 

13 

8: 

1 

1456 

0 

0 

t 

1801 

6 

16 

15 ; 

1120 

0 

0 

i 

1465 

6 

16 

i 

4 

1810 

13 

8 

A 

8 

1129 

6 

16 

| 

1474 

13 

8 

1820 

0 

0 

| 

1138 

13 

8 i 

¥ 

1484 

0 

0 

i 

1829 

6 

16 


1148 

0 

0 

20 

1493 

6 

16 

| 

1838 

13 

8 

l 

1157 

6 

16 

¥ 

1502 

13 

8 


1848 

0 

0 

| 

1166 

13 

8 

l 

4 

1512 

0 

0 

I 

1857 

6 

16 

1 

1176 

0 

0 

1 

1521 

6 

16 

25 

1866 

13 

8 

1 

1185 

6 

16' 

i 

1530 

13 

8 

i 

¥ 

1876 

0 

0 

16 

1194 

13 

8 

t 

1540 

0 

0 

1 

4 

1885 

6 

16 

1 

8 

1204 

0 

o! 

i 

1549 

6 

16 

3 

¥ 

1894 

13 

8 

1 

¥ 

1213 

6 

16 

i 

1558 

13 

8 

¥ 

1904 

0 

0 

| 

1222 

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8 

21 1 

1568 

0 

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f 

1913 

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i 

1232 

0 

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i! 

8 

1577 

6 

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3 

4 

1922 

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4 i 
8 

1241 

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i 

1586 

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¥ 

1932 

0 

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1111250 

13 

8 


1596 

0 

0| 

26 | 

1941 

6 

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A* 

































































































110 


THE PRACTICAL MINERS 


SILVER ASSAY TABLE. —Continued. 


Assay 

1 

Per Ton. 

| Assai 

r Per Ton. 

Assa: 

l 

r Per Ton. 

grs. 

oz. 

dwt 

grs. 

1 grs. 

oz. 

dwt 

■ grs. 

grs. 

oz. 

dwt 

. grs. 

26J 

1950 

13 

8 

' 305 

2296 

i c 

) 0 

35f 

12641 

[ 6 

16 

1 

4 

1960 

0 

0 

f 

2303 

i 6 

> 16 


265C 

) 13 

8 

1 

1969 

6 

16 

1 31 

2314 

13 

: 8 

I 

I266C 

l 0 

0 1 

i 

1978 

13 

8 

1 4 

2324 

0 

' 0 

i 

2668 

> 6 

16 

I 

1988 

0 

0 

1 

4 

2333 

6 

■ 16 

1 4 

, |2678 

: 13 

8 

1 

11997 

6 

16 

f 

2342 

13 

8 

36 

! 12688 

0 

0 

4 

2006 

13 

8 

4 

2352 

0 

0 

i 

[2697 

6 

16 

27 

2016 

0 

0 

t 

2361 

6 

16 

? 

4 

2706 

13 

8 

i 

8 

12025 

6 

16 


2370 

13 

8 

| 

2716 

0 

0 

1 

4 

2034 

13 

8 

4 

2380 

0 

0 

1 

2 

2725 

6 

16 

I 

2044 

0 

0 

32 

2389 

6 

16 


2734 

13 

8 

1 

2 

2053 

6 

16 

i 

8 

2398 

13 

8 


2744 

0 

0 

t! 

2062 

13 

8 

1 

4 

2408 

0 

o! 


2753 

6 

16 

|,| 2072 

0 

0 

f 

2417 

6 

16 

37 

2762 

13 

8 

S' , 

2081 

6 

16 

4 

2426 

13 

8 

i 

2772 

0 

0 

28 

2090 

13 

8 

t 

,2436 

0 

0 

x 

2781 

6 

16 

i 

8 

2100 

0 

0 

t 

2445 

6 

16 

4 - 

| 

2790 

13 

8 

i 

2109 

6 

16 

4 

2454 

13 

8 

4 

2800 

0 

0 

f 

2118 

13 

8 

33 

[2464 

0 

0 


2809 

6 

16 

\ ! 

2128 

0 

0 

i 

8 

2473 

6 

16 

I 

2818 

13 

8 

f 

2137 

6 

16 

i 

2182 

13 

8 

¥ 

2828 

0 

0 

3 I 
*; 

2146 

13 

8 

f 

[2492 

0 

0 

38 

2837 

6 

16 

4 

2156 

0 

0 

l 

¥ 

2501 

6 

16 

i 

p 

2846 

13 

8 

29 

1 

2165 

6 

16 

¥ 

25 JO 

13 

8 

o 

2856 

0 

0 


2174 

13 

8 


2520 

0 

0 

| 

2865 

6 

16 

,i 

2184 

0 

0 

4 

2529 

6 

16 

1 

2 

2874 

13 

8 

I 

2193 

6 

16 

34 

2538 

13 

8 

f 

2884 

0 

0 

41 

2202 

13 

8 

i 

8 

2548 

0 

0 


2893 

6 

16 

f 

2212 

0 

0 

4 

2557 

6 

16 

4 2902 

13 

8 

1 

2221 

6 

16 

1 

2566 

13 

8 

39 

2912 

0 

0 

_ 4 i 

2230 

13 

8 

4 

2576 

0 

0 

1 

p 

2921 

6 

16 

cc 

o 

2240 

0 

0 

f 

2585 

6 

16 

o 

\ 

2930 

13 

8 

J, 

8 

2249 

6 

16 


2594 

13 

8 


2940 

0 

0 

1 

4 

2258 

13 

8 

4 

2604 

0 

0 

1 

o 

2949 

6 

16 

f 

2268 

0 

0 

35 

2613 

6 

161 

A 

, f 

2958 

13 

8 

1 !l 

2 

2277 

6 

16 

i 

8 

2622 

13 

8 


2968 

0 

0 

5 

8 II 

2286 

13 

A 

1 

¥ 

2632 1 

o 

o|_ 


2977 

6 

16 



































































































OWN BOOK AND GUIDE, 


111 


SILVER ASSAY TABLE. —Continued. 


Assay 

Per Ton. 

Assay 

Per Ton. 

Assay 

Per Ton. 

grs. 

oz. 

dwt. 

grs. 

grs. 

oz. 

dwt. 

I grs. 

grs. 

oz. 

dwt 

grs. 

40 

2986 

13 

8 

44f 

3332 

0 

0 

491 

3677 

6 

16 


2996 

0 

0 

i 

3341 

6 

16 

I 

3686 

13 

8 

i 

3005 

6 

16 

7 

■g" 

3350 

13 

8 

i 

3696 

0 

0 

| 

3014 

13 

8 

! 45 

3360 

0 

0 

f 

3705 

6 

16 


3024 

0 

0 

8" 

3369 

6 

16 

% 

3714 

13 

8 

t 

3033 

6 

16 

1 

A 

3378 

! 13 

. 8 

i 

3724 

0 

0 

1 

13042 

13 

8 

| 3388 

0 

0 

50 

3733 

6 

16 

i 

[3052 

0 

0 


3397 

6 

16 


3742 

13 

8 

41 

13061 

6 

16 


3406 

13 

8 


3752 

0 

0 

i 

8 

13070 

13 

8 


3416 

0 

0 

1 

3761 

6 

16 

1 

4 

3080 

0 

0 


3425; 

6 

16 

| 

3770 

13 

8 


3089 

6 

16 

46 ! 

13434 

13 

8 


3780 

0 

0 

i 

3098 

13 

8 

i 

8 | 

3444 

0 

0 


3789 

6 

16 

t 

3108 

0 

0 

i\ 

3453 

6 

16 

i 

3798 

13 

8 

1 

3117 

6 

16 

« 

3462 

13 

8 

51 

3808 

0 

0 

$ 

3126 

13 

8 

i 

3472 

0 

0 

i ' 

3817 

6 

16 

42 

3136 

0 

0 


3481 

6 

16 

i 

3826 

13 

8 

i 

3145 

6 

161 

I 

3490 

13 

8 

I 

3836 

0 

0 

i 

3154 

13 

8 

i 

3500 

0 

0 

h 

3845 

6 

16 

f 

3164 

0 

0 

47 ! 

3509 

6 

16 

f 

3854 

13 

8 

i 

3173 

61 

]6 

! i 

8" ! 

3518 

13 

8 

1 

3864 

0 

0 

■§• 

3182 

13 

8 

i 

3528 

0 

0 

7 

•S’ 

3873 

6 

16 


3192 

0 

0 


35371 

6 

16 

52 

3882 

13 

8 

I 

3201 

6 

16 

! 1! 

3546 

13 

8 


3892 

0 

0 

43 

3210 

13 

8! 

! t 

3556 

0 

0 


3901 

6 

16 

! i 

3220 

0 

0 

1 3 

3565 

6 

16 

1 

3910 

13 

8 

i 

3229 

6 

16 

•g" 

3574 

13 

8 

h 

3920 

0 

0 

I 

3238 

13 

8' 

48 

3584 

0 

0 

f 

3929 

6 

16 ! 

i 

3248 

0 

0 

1 

8 

3593 

6 

16 


3938 

13 

8 


3257 

6[ 

16 

* 

3602 

13 

8 


3948 

0 

0 

I 

3266 

13 i 

8 


3612 

0 

0 

53 

3957 

6 

16 

i 

3276 

0 

0 

1 

2 

3621 

6 

16 

i 

3966 

13 

8 

44 

3285 

6 

16 

f 

3630 

13 

8 


3976 

0 

0 

i 

3294 

13 

8 

1 

3640 

0 

0 

1 

3985 

6 

16 

i 

3304 

0 

0 

l 

3649 

6 

16 

1 

2 

3994 

13 

8 


3313 

61 

16 

49 

3658 

13 

8 

5. 

8 

4004 

0 

0 

i 

5 

3322 

13| 

8! 

i 

8 

3668 

0 

0 

1 

4013 

6 

16 












































































112 


THE PRACTICAL MINERS' 
SILVER ASSAY TABLE.— Continued. 


Assay 

Per Ton. 

grs. 

oz. 

dwt. 

grs. 

53* 

4022 

13 

8 

54 

4032 

0 

0 

i 

4041 

6 

16 


4050 

13 

8 

I 

4060 

0 

0 

* 

4069 

6 

i 

t 

4078 

13 

i 

4088 

0 

o! 


4097 

6 

16 

55 

4106 

13 

8 

i 

4116 

0 

0 

i 

4125 

6 

16 


4134 

13 

8 

* 

4144 

0 

0 

1 

4153 

6 

16 

* 

4162 

13 

8 


41721 

ol 

0 ! 


Assay 

Per Ton. 

grs. 

oz. 

dwt. 

grs. 

56 

4181 

6 

16 

8 

4190 

13 

8 


4200 

0 

ol 

| 

4209 

6 

16 

1 

4218 

13 

8 

t 

4228 

0 

0 


4237 

6 

16 

* 

4246 

13 

8 

57 

4256 

0 

0 

i 

8 

4265 

6 

16 

1 

4 

4274 

13 

8 

I 

42841 

0 

0 

i 

4293! 

6 

16 

1 

4302 

13 

8 


43121 

0 

0 

8 

4321| 

6 

16 

58 1 

4330! 

131 

8 


Assay 

Per Ton. 

grs. 

oz. 

dwt. 

grs. 

58* 

4340 

0 

0 

| 

4349 

6 

16 


4358 

13 

8 

* 

4368 

0 

0 

t 

4377 

6 

16 

i 

4386 

13 

8 

* 

4397 

0 

0 

59 

4406 

6 

16 

j. 

6 " 

4415 

13 

8 

* 

4424 

0 

0 

| 

4433 

6 

16 

* 

4442 

13 

8 

1 

4452 

0 

0 

3 

4 

4461 

6 

16 


4470 

13 

8 

60 

4480 

0 

0 


Copper ores should be computed at twenth-one cwt. to the 
ton the surplus being allowed for waste in carriage, &c. 























































OWN BOOK AND GUIDE. 


113 


POWER OF STEAM ENGINES. 

Rules for discovering the power of Steam Engines. 

1. Square the diameter of the cylinder, multiply the sum 
by .7854* and the product by 16f, lastly, multiply again by 
144J, and the last product will show the number of pounds 
the engine lifts a foot high in a minute. 

2. A horse is estimated to raise 500 lbs. 64 feet high, or 
1000 lbs. 32 feet high, or 32000 lbs. 1 foot high in a minute, 
consequently if the last product be divided by 32000, the quo¬ 
tient will show the number of horses required to equal the 
power of the engine. 

EXAMPLE. 

What is the power and horse power of a steam engine, the 
cylinder being 46 inches in diameter ? 

46 X 46=2116 
.7854 


1661.9064 

10 


16619.0640 

144 


32000')2393145.2160(75 
224000 


153145 

160000 


ANSWER. 

Engine lifts 2393145 lbs. one foot high in a minute, equal 
to 75 horses nearly. 

*The established ratio of the diameter; or look in the table, page 
117, where the square inches contained in a cylinder are given, and 
take out the number standing opposite the given diameter. 

t That is, considering the power equal to 15 lbs. to an inch, and al¬ 
lowing 5 lbs. or one-third for friction. 

X Considering the stroke to be 8 feet, and the engine to go 9 strokes 
per minute. 








114 


THE PRACTICAL MINERS’ 


WATER ENGINES. 

Rules for discovering the power of a Water Engine. 

1. Multiply the length, breadth and depth of the bucket 
together, and divide by 282, (the number of cubic inches in a 
gallon, beer measure,) multiply the quotient by 10| lbs. or 10 
lbs. 3.2 oz. or 10.2 lbs. the weight of a gallon of water* 

2. Multiply the diameter of the wheel by 3.1416 (the ratio 
of the circle,) and divide the product by the circular space oc¬ 
cupied by each bucket—the quotient will show the number 
of buckets contained in the wheel. 

3. Multiply the third partf of the number of the buckets by 
the weight of water contained in one, then 

4. For the leverage. From the radius or half the diame¬ 
ter, deduct the length of the crank and one-third of the remain¬ 
der will be the operative length of the lever; multiply the 
weight of water in one-third of the wheel by this length (tak¬ 
ing the feet for the whole number of the multiplier,) and the 
product will show the full or entire power. Lastly, from this 
product cast off one-fifth for friction,J and the remainder will 
show the net or real power of the wheel. 


example. 

Required the power of a water-wheel, the diameter being 
46 feet, the buckets 30 inches long, 12 inches deep and 6 in¬ 
ches wide, with 1J inch, between each bucket, and the crank 
3 feet long ? 


* The result will be the same if the operation is clone by the wine gal- 
t0 contain 281 cubic inches ’ and ,o wei « h 81bs - 6 68 

tendbathaTfw' 11 '° f T™ res P ec,in S «>«, some Persons con- 
tendmg that two-fifths the number of buckets are full at a time, but one- 

third is the most general and the most reasonable proportion. 

onifirih\nm in enS ‘. nee ( '? are not unanimously agreed, some allowing 
e-fiflh, some one-fourth, and some even one-third of the power for 
riction. It is true the distance the wheel is placed from the work and 
-contingent circumstances must be taken into considered ; Zt 

nefZZZh ’ Where the Wheel draWS Cl0Se> is very 






OWN BOOK AND GUIDE. 


115 


OPERATION. 

1. To find the quantity and weight of water in each bucket. 

30 X 12X6=2160-7-282=7.66 X 30.2=78.13. 

2. To find the number of buckets contained in the wheel. 

46X12=552X3.1416=1734 (6+1*) -^7.25=239. 

3. To find the weight of water on | of the wheel. 

239-7-3=80x78.13=6250. 

4. To find the power of the lever. 

46-f-2=23—3=20 -h3=6.66, and 
6250X6.66=41625. 

Lastly, for friction 
5)41625 
8325 

Ans. 33300 lbs. the actual power of the wheel. 

To find the depth at which a wheel will draw a column of 
water in a lift of pumps of any given dimensions. 

Rule.— Find the power of a wheel by the foregoing me¬ 
thod, then from the table, page 119, take out the weight of 
water in a fathom of the given size pump. Divide the power 
of the wheel (in pounds) by this number, and the quotient 
will show the fathoms. 

EXAMPLE. 

The power of the fore-mentioned wheel is 33300 lbs. how 
deep will she draw in a 12 inch lift of pumps ? 

294.53)33300(113 

Ans. 113 fathoms. 

To find the horse-power of a wheel. 

Rule.— Multiply the power (found by the given rule, page 
114,) by the number of revolutions made by the wheel in a 
minute, and this product by the length of the stroke in feet, 
or double the length of the crank, divide the last product by 
32000, and the quotient will show the number of horses re¬ 
quired to equal the power of the wheel. 



116 


THE PRACTICAL MINERS’ 


EXAMPLE. 

The fore-mentioned wheel is allowed to make seven revo¬ 
lutions in a minute, required the horse power? 

33300 

7 


233100 

6 


32000)1398.600(44 

128 

118 

128 


Ans. 44 horse-power, nearly. 





own book and guide. 


117 


TABLE 

Shotting the square inches contained in a cylinder or circle 
from ten to seventy-three inches in diameter. 


Diam¬ 
eter of 
Cylin¬ 
der. 

Square 
Inches. 

Diam¬ 
eter of 
Cylin¬ 
der. 

Square 

Inches. 

Diam¬ 
eter of 
Cylin¬ 
der. 

Square 

Inches. 

Diam- 
i eter of 
Cylin¬ 
der. 

Square 

Inches. 

10 

78.54 

26 

530.93 

42 

1388.59! 

58 

2642.00 

11 

95.03 

27 

572.56 

43 

1452.20! 

59 

2734.00 

12 

113.10 

28 

615.75 

44 

J 520.53 

60 

2827.44 

13 

132.73 

29 

660.20 

45 

1590.43 

61 

2922.47 

14 

153.94 

30 

706.86 

46 

1661.91! 

62 

3019.00 

15 

176.71 | 

31 

754.771 

! 47 

1735.00 

63 

3117.25 

16 

201.06! 

32 

804.251 

48 

1809.56 

64 

3217.00 

17 

226.98 

33 

855.301 

49 

1885.74 

65 

3318.31 

18 

254.47 

34 

907.92 

50 

1963.50 

66 

3421.20 

19 

283.54 

35 

962.00 

51 

2042.82 

67 

3526.66 

20 

314.16! 

36 

1017.88 

52 

2123.72 

68 

3651.69 

21 

346.36 ! 

37 

1075.20) 

53 

2206.19 

69 

3739.29 

22 

380.13 

38 

1134.00! 

54 

2290.23 

70 

3848.46 

23 

415.47 

39 

1194.60 

[ 55 

2375.83 

71 

3959.20 

24 

452.39 

40 

1256.64 

56 

2463.00 

72 

4071.51 

25 | 

490.88 |i 

41 

1320.26 | 

57 

2651.761 

73 

4185.40 


Note. —The annexed table, of the quantity and weight of water 
contained in six feet of pump, (page 119,) may be proved or extended 
by the following rules, viz : 

Square the diameter of the pump and multiply the product, first by 
the decimal .7854, again by the length of the pump in inches, and 
divide by 231, the whole numbers in the quotient will show the wine 
gallons. Then, to find the cubic feet, divide the solid inches by 1728. 
Again, to find the weight, multiply the cubic feet by 1000, and divide 
the product by 16. 







































118 


THE PRACTICAL MINERS’ 


EXAMPLE. 

How many pounds, wine gallons and cubic feet, are con¬ 
tained in a cylinder or pump 12 inches in diameter and 6 feet 
in length ? 

To find the Wine Measure. 

12 X 12== 144 Square of diameter. 
.7854 Multiplier. 


113.0976 

6 


678.5856 

12 

Cubic inches in a- 

wine gallon=231)8143.0272(35.2512 

4 


1.0048 


Answer.—35 gals. 1 qt. 

To find the Cubic Feet. 

( Inches in a 

\ cubic foot.—1728)8143.0272 Inches as before. 


4.7124 Cubic feet. 


To find the Pounds. 

4.7124 Cubic feet as before, 

1000 oz. weight of a cubic foot of water. 

16)4712.4000 


294.525 lbs. weight. 












OWN BOOK AND GUIDE. 


119 


A TABLE 

Showing the weight , wine gallons , and cubic feet of water con¬ 
tained in 6 feet of pump, from 4 to 20 inches in diameter. 


1 Diameter 

1 of Pump. 

Weight. 

Wine 

Measure. 

Cubic 

Feet. 

Diameter 

of Pump. 

Weight. 

Wine 

Measure. 

Cubic 

Feet. 

ins. 

lbs. dec. 

gal 

qts 

pts 

ft. dec. 

ins. 

lbs. dec. 

gal 

qts 

pts 

ft. dec. 

4 

32.75 

3 

3 

1 

.522 

12* 

306.95 

36 

2 

1 

4.910 

44 

36.95 

4 

1 

1 

.591 

12| 

319.60 

38 

1 

0 

5113 

44 

41.42 

4 

3 

1* 

.662 

12} 

332.51 

39 

2 

1 

5.319 

44 

46.15 

5 

2 

0 

.738 

13 

345.68 

41 

1 

1 

5.530 

5 

51.14 

6 

0 

1 

.818 

13} 

359.10 

42 

3 

1 

5.745 


56.38 

6 

3 

0 

.902 

134 

372.78 

44 

2 

1 

5.960 


61.87 

7 

1 

H 

.989 

13} 

386.72 

46 

0 

1 

6.187 


67.63 

8 

0 

Oh 

1.082 

14 1 

400.90 

48 

0 

0 

6.414 

6 

73.63 

8 

3 

0 

1.178 

14i! 

415.35 

49 

2 

1 

6.645 

61 

79 90 

9 

2 

0 

1.278 

144 

430.00 

51 

1 

1 

6.880 

61 

86.42 

10 

1 

0 

1.382 

14} 

445.00 

53 

0 

1 

7.119 

61 

93.20 

11 

0 

0 

1.491 

15 1 

460.23 

55 

0 

1 

7.363 

7 

100.22 

12 

0 

0 

1.603 

m 

475.69 

56 

3 

1 

7.610 

n 

107.51 

12 

3 

0 

1.720 

154* 

491.42 

58 

3 

0 

7.862 

71 

115.00 

13 

3 

0 

1.840 

154 

507.40 

60 

2 

1 

8.117 

7f 

122.85 

14 

2 

1 

1.965 

16 

523.63 

62 

2 

1 

8.379 

8 

130.90 

15 

'2 

1 

2.094 

I64 

540.13 

64 

2 

1 

8.641 

81 

139.22 

16 

2 

1 

2.227 

I 64 

556.87 

66 

2 

1 

8.909 

81 

147.78 

17 

2 

1 

2.354 

16} 

573.88 

68 

2 

1 

9.181 

81 

156.60 

18 

2 

1 

2.505 

17 

591.13 

70 

3 

0 

9.457 

9 

165.68 

19 

3 

0 

2.650 

174 

608.65 

72 

3 

0 

9.739 

91 

175.00 

20 

3 

1 

2.800 

174 

626.42 

75 

0 

0 

10.022 

91 

184.60 

22 

0 

0 

2.953 

17| 

644.67 

77 

0 

1 

10.310 

91 

194.45 

23 

J 

0 

3.110 

18 

662.73 

79 

1 

0 

10.602 

10 

204.54 

24 

1 

1 

3.272 

184 

681.26 

81 

2 

0 

10.899 

101 

214.90 

25 

2 

1 

3.438 

184 

700.00 

83 

3 

0 

11.142 

101 

225.51 

27 

0 

0 

3.607 

184 

719.10 

|86 

0 

1 

11.504 

101 

236.37 

28 

1 

0 

3.781 

19 

738.40 

88 

1 

1 

11.813 

11 

247.50 

29 

2 

1 

3.959 

194 

757.96 

90 

3 

0 

12.126 

111 

258.87 

30 

3 

1 

4.141 

194 

777.78 

93 

0 

l 

12.443 

111 

270.51! 

32 

1 

1 

4.327 

194 

797.85 

95 

2 

0 

12.764 

111 

280.40 

33 

2 

1 

4.518 

20 

818.18 

97 

3 

1 

13.090 

12 

294.531 

35 

1 

0 

4.712 



1 





































120 


THE PRACTICAL MINERS’ 

traverse surveying. 

It cannot be disputed that nearly all the managers of mines, 
of every description in America, have been and are now 
selected from those that have been brought up as working 
miners from their youth, and from foreign countries ; while 
the Americans themselves, who own the lands and minerals, 
prefer other professions, such as lawyers and doctors. It is 
true that it is necessary that every person who has charge of 
mines should possess a good deal of practical knowledge, to 
enable him to fix the value or fair prices of the different work 
which is done by contract, and to know what a fair day’s 
work is, and to tell how much coal or any kind of earth or 
minerals a man can remove in the various seams in mines, 
each day and while we recommend practical knowledge, we 
do not intend to slight its near kinsman, theoretical knowledge, 
but would suggest that they go hand-in-hand together. And 
we will beg leave to say, for the encouragement of those that 
do not possess as much practical knowledge as others, and 
wish to follow a mining occupation, not to be discouraged 
from prosecuting his incumbent and laudable studies, and 
qualify himself for performing the high and paramount duties 
of a mine agent with credit to himself, and advantage to his 
* em ployers, and benefit to his country. It is questionable, with 
the author of this work, whether a mining traverse has ever, 
up to the present time, been trigonometrically solved in this 
country, and all the instructions given to this period for find¬ 
ing the ultimatum of a course of surveyings has been by con¬ 
struction or instrumental operation. But we now ask to be 
allowed to recommend and show a more excellent way of 
performing the whole by computation or by figures. The 
trigonometrical method of working a course of surveying re¬ 
duces the whole, however numerous and diversified, into^two 
numbers, for the four columns of eastings, westings, northings 
and southings being added up separately, and then the lesser 
deducted from the greater of the opposite cardinal points, re¬ 
duces the whole into two numbers, forming the base and 
perpendicular of the great triangle, and are necessarily right 


OWN BOOK AND GUIDE. 


121 


angle cardinal bearings, such as easting and southing, or 
northing and westing, as the case may be; and our next and 
last operation is to find the hypothenuse and an angle cor¬ 
responding with these two sides, which hypothenuse and 
angle is the final line, or course of the survey. 

EXAMPLE. 

A traverse has been worked, the columns added up, and the 
westing subtracted from the easting, showing the excess of 
easting to be 346 feet, and the southing subtracted from the 
northing, the difference proved the excess of northing 419 
feet 5 inches. 

OPERATION. 

Find the hypothenuse by square root. 

Rule.— Add the sum of the squares of the two sides 
together, and extract the square root of their sum. 


346 

419.4 

346 

419.4 

2076 

16776 

1384 

37746 

1038 

4194 


16776 

119716 



175896.36 


119716 


295612.36(543.7 


25 12 


104) 456 8.4 


416 

1083) 4012 
3249 


10867) 76336 
76059 


267 


Answer.—Hypothenuse 543 feet 8 inches. 












122 


THE PRACTICAL MINERS’ 


Find, the angle by proportion. 


ft. 

in. ft. 

ft. 

f 419 

5 gives 346 what 

will 6 give ? 

12 

12 

12 

— 

— 

_ 

5033 

4152 

72 


72 



8304 



29064 



5033)298944(59.39 in. or 4 ft. 11.39 in. 
25165 


47294 

45297 


19970 

15099 


48710 

45297 


4413 


Then by inspection in the second table, page 80, this 
quotient of 4 feet 11.39 inches will be found standing oppo¬ 
site 39° 30', which is the bearing or sum of the angle oppo¬ 
site the shortest side of the great triangle. 

Answer Hypothenuse, or direct length from beginning to 
end, 543 feet 8 inches. Bearing, or direction from be¬ 
ginning to end, 39° 30' east of north. 


REMARKS. 

In carrying out this system practically, after we have laid 
down this grand or final line at surface, and fixed a mark at 
the extreme end of the line which has been measured off 
from the starting point, 543 feet 8 inches, on the bearing, 
390 30' east of north, (or 50° 30' north of east, the comple¬ 
ment,) we are furnished with a double means of proving if 









OWN BOOK AND GUIDE. 


123 


this length and angle has been correctly laid down, by 
measuring off, due north, 419 feet 5 inches from the start, 
and then placing the theodolite or compass on the end of that 
line and measuring off due east 346 feet; consequently, if the 
whole has been well done, the last mark will exactly agree 
in both cases; or should the ground be more favorable, we 
may avail ourselves of the convenience of laying off the east 
line first, and the north line last, which will bring us to the 
same point. One great advantage of these proof lines will 
appear, when we take into consideration that most of the in¬ 
struments used in mines for taking horizontal angles have no 
vernier scale for reading off the fraction of the angle, and, 
therefore, if the bearing falls between any quarter, or half of 
a degree, the surveyor must depend on the judgment of his 
eye for the division, and let it be known that an error of one 
quarter of a degree in 100 feet amounts to 5 inches and a 
decimal of .23596, or upwards of 2 feet 7 inches in a line of 
100 fathoms, hence the value of having this most satisfactory 
and convenient check for the laying down of the last grand 
line ipust be manifest to every observer, and should never be 
neglected. 

LOGARITHMS. 

Should the practitioner wish to prove the finding of the 
angle and hypothenuse by logarithms, the following is the 


rule: 

From less side 346 and radius=.12.5390761 

Subtract longest side, 419.4=. 2.6227140 

Logarithm tangent of 39° 30'. 9.9163621 

Rule for the Hypothenuse. 

From less side and radius, (as before).12.5390761 

Subtract sine of 39° 30'. 9.8035105 

Logarithm of 543.8, nearly. 2.7355656 












124 


THE PRACTICAL MINERS’ 

The rules expressed at length, read thus: 

For the Angle. 

Add the radius to the logarithm of the less side, and from 
the sum subtract the logarithm of the greatest side, the re¬ 
mainder or sum will be the tangent of the angle opposed to 
the less side. 

For the hypothenuse. 

Add the logarithm of the given side to the sine of the angle 
opposite to the side required, and from the sum subtract the 
sine of the angle opposed to the given side, the remainder will 
be the logarithm of the side required. 

System. 

There is much propriety in the remark, that “system is the 
handmaid of science,” and the term may be considered as 
used in contradistinction to disorder, irregularity, or random. 
The man who would excel in the important work of subter¬ 
raneous surveying should have a system, and a good one. It 
is true, men are apt to be bigoted in this matter, and think so 
highly of their own system as to despise all others, but cer¬ 
tainly we must admit that a bad or imperfect system is better 
than no system at all. He who has no fixed rule is liable to 
error every step he takes. We would recommend the young 
surveyor to adopt a system in keeping his register or survey¬ 
ing book underground, so that his subterranean surveys may 
be perfectly clear and comprehensible, not only to himself but 
to all practical men. Let us suppose we have to survey a 
level driven on the course of the lode, where there are several 
cross cuts driven off to the right and left. I would advise the 
student to keep the number of his drafts on the main line, or 
course of the lode, in regular numerical order, and when he 
has to branch off on a cross cut, let him make the necessary 
mark, and call the first draft in that cross-cut number 1, and 
so on in succession to the end of it. On his return to the 
mark where he departed from the main line, let the surveying 
on the cross-cut stand in the book as a parenthesis, and let 


OWN BOOK AND GUIDE. 


125 


him resume his course on the lode, numbering his drafts in 
order from where he branched off. By this system, he will 
have no turning from one place to another in his book-all 
will be regular; and if the main course or any other should 
be required to be copied separately, in the fair surveying book, 
it can easily be done. Moreover, should a diagram or geome¬ 
trical plan of the level and all its windings, and drifts or cross 
diivings be required, by this mode of entry everything will 
appear in its proper place. Another part of the “ system ” is, 
to let the sight or vane fixed at 360° always take the lead, and 
the surveyor’s eye placed at the opposite vane, except when 
taking back observations. This will be found under the head 
of remarks connected with the “ converting table,” and in hori¬ 
zontal surveying, let two drafts be made from every station, 
which will expedite the work, as the surveyor will only have 
to wait for the settling of the needle once, instead of twice by 
the other method. 

Surveying without the magnetic needle. 

This is a valuable modern discovery in mine surveying and 
as necessity is the mother of invention,” the general intro¬ 
duction of railways and tram-roads in mines, drove the sur¬ 
veyor to seek some substitute for the needle, which the attrac¬ 
tion of iron rendered useless, and he has happily succeeded. 
This method of surveying cannot be performed with the com¬ 
mon compass; but the best circumferentors are now made 
with an external graduation and vernier scale on the theodo¬ 
lite principle, on purpose for the performance of this work.— 
Mr. VV. Cox, (from Arnold’s, London,) of Devenport, makes 
these instruments in a superior style to any other in the west 
of England. 

The method of surveying on this principle differs from the 
magnetic method chiefly in one particular, namely, that in 
every fresh draft, the position of the bearing must be ascer 
tained by the back observation in the direction of the sights, 
and the angle made at the old station must be obtained and 
6 


THE PRACTICAL MINERS' 


126 

preserved at the new stations, and this is evident because we 
have no magnet for our guide. For example:—suppose we 
are surveying over a railway in a level and the last observation 
was 259°, after measuring the length, the instrument is re¬ 
moved and carried forward to the place of the light where the 
angle was taken, and a mark and light left at the old station. 
Then, after the instrument lias been adjusted in his true place, 
the next act of the surveyor is to place the centre of the ver¬ 
nier on 259°, as it stood at the old station, and if the instru¬ 
ment does not move by rack-work, he must keep all firm with 
his hands and turn the head towards the last station until the 
candle is seen through the sights, he then removes behind the 
instrument and moves the sights in the direction for the next 
draft, where the assistant is holding a light for the purpose, 
(the graduation being fixed,) and this new draft gives (say) 
270^°, showing a difference between the two drafts of ll£°. 
Although this process is somewhat tedious in description, it is 
simple in practice, and the history of one draft is as well as a 
hundred, and we may observe that with proper care and judg¬ 
ment this is the most perfect method of surveying, because 
there is no risk of attraction, and as the circle is much larger 
than the inside plate, and the divisions more distinct together 
with the vernier scale being applied, the angle can be read off 
to one or two minutes, a nicety which cannot be attained by 
the needle in the common way. It is hardly necessary to 
state, that in order to obtain the bearing, there must be at least 
one draft in the traverse where the needle must be brought, 
into play, and this draft will determine the polarity or direc¬ 
tion of the whole. Further, let it. be remarked, that a survey 
may be resolved into bearings and worked trignometricalJy 
when this method is used as by the needle. Suppose a case 
that we are about to survey over a railway, but there is space 
enough clear of iron for the first draft, and taking the observa¬ 
tion with the needle we find the north point (a right hand com¬ 
pass) stand at 176|°, we then fix the outer circle with the 
vernier precisely at the same point, and then throwing off the 


127 


OWN BOOK AND GUIDE. 

needle, perform all the remainder of the traverse by means of 
the outer circle, hence it will be evident then, if the outward 
circle is also graduated towards the right hand, that the whole 
course will come under the immediate operation of the “con¬ 
verting table,” as if the work had been performed with the 
needle, and if the graduation should be reversed, the “left- 
a nd bearings will apply accordingly, regard being had to in¬ 
version in both cases. This instrument is also well adapted 
for taking the bearing of diagonal or underlaying shafts, hav¬ 
ing a lift of iron pumps, a job that has often baffled the skill 
and ingenuity of surveyors, and occasioned numerous and 
most serious errors. The operation may be performed thus • 
Suppose we are in the 60 fathom level, and from thence to the 
100 , the shaft was sunk on the course of the lode, on an un¬ 
derlay of 3 feet per fathom northerly. By applying the in¬ 
strument at some point in the level near the -shaft, (but far 
enough away to be free from attraction by the pump,) we find 
the bearing by the needle, to a point opposite the shaft, to be 
due west and the vernier on the outer rim standing at 90°, we 
then remove the instrument to the shaft, where the light was 
held, and adjust the back observation, as before directed, hav¬ 
ing 90° on the outer rim and the needle thrown off as useless, 
because we are now close to the pumps. A light is to be car¬ 
ried down the shaft as far as it can be seen, and after the gra¬ 
duated circle has been screwed fast, the rack is applied and 
the sights turned until we cut the candle in the bottom of the 
shaft, this being done we examine and read off the degree 
against the point of the vernier, which proves to be (say) 
187f°, now as when the instrument stood in a due west posi¬ 
tion the outer circle stood at 90°, and in taking the bearing it 
stood at 187J°, therefore by subtracting 90° from 187£° we 
find the gain to the right hand of west is 97}°, and the under¬ 
lay being northerly, the true bearing of the shaft is 7|° east 
of north. The imperative call for accuracy in cases of this 
kind, will be seen when it is considered that the diagonal part 
of this shaft is upwards'of 40 fathoms, and the underlay 3 feet 


128 


THE PRACTICAL MINERS 


in a fathom, consequently the whole base is more than 20 fa¬ 
thoms, and an error in the bearing has the same effect on the 
survey as if it had been made in taking a horizontal draft of 
20 fathoms long, and on which an error of 4° would throw 
the end of the line nearly 9 leet too far either to the right or 
left. 

Should a surveyor be called to do a job of this kind in the 
absence of a suitable instrument, he may accomplish it in the 
following manner:—let him fix a cross-staff in such a position 
that through one pair of sights, he can see the light in the 
shaft and in the line of the other pair, he has the compass 
fixed in the level out of the way of the attraction, consequent¬ 
ly the light in the shaft and the compass in the level are two 
objects forming a right angle with his cross-staff, he then re¬ 
quests his assistant to look at a light held immediately over 
the head of his cross-staff, through the sights of the compass, 
and he finds this (say) 12° north of west, and as the bearing 
of the shaft is exactly at right angles with this line, if the un¬ 
derlay is northerly, the bearing of the shaft will be 12° east 
of north; if southerly, 12° west of south. The best cross¬ 
staffs or instruments for the express purpose of taking right 
angles, are now made of a hollow cylindrical shape, of brass, 
with cuts or apertures, for taking the observation, but a sub¬ 
stitute may be used on a pinch by drawing two lines at right 
angles on a board, about 6 inches square and an inch thick, 
let these be cut half an inch deep with a fine saw and then fix 
it on a 3 feet stand, if the lines are truly drawn and cut, this 
rough instrument will serve until a better one can be pro¬ 
cured. 

Construction. 

The old method in laying down a traverse was by drawing 
a parallel line, and removing the protractor at every draft. 
The evils of this practice are too glaring to require remark. 
Fix your protractor, and lay off as many drafts as will come 
within the convenient range of your parallel ruler; number 


OWN BOOK AND GUIDE. 


129 


them in order as they stand in your surveying book; remove 
the protractor, and lay off the first draft from the centre direct; 
then apply the protractor to the centre and No. 2, and make 
the parallel movement until you touch the end of the last line 
or No. 1 , and then draw and point off the length of No. 2, 
and so on through all the drafts you have pointed off from 
the protractor. 

The advantage of laying down or pointing off a number of 
drafts at one fixing of the protractor and then applying them 
in their true length and position, is most conspicuous, and the 
geometrician will testify of its superiority, both as it regards 
accuracy and expedition. 

CONVERTING TABLE. 

Remarks on the following table for converting the degrees 
recorded in the surveying book of an underground survey 
into the bearings. 

All practical men are aware of the difficulty, hazard and 
delay that attends an attempt to obtain the bearing of every 
draft underground in a long and complicated survey. The 
best process is to record the degree, or angle only at which 
the needle settles, and after the work is finished underground, 
then convert the various angles into the real bearings or true 
direction of each draft, and we may remark, that the bearings 
must be obtained if the work is to be mathematically proved. 
But as it is not an easy matter to turn a long course of survey¬ 
ing into the bearings, with an assurance of being correct, this 
table has been constructed for that express purpose, and its 
utility, simplicity and perfection has been acknowledged by 
many practical men. 

Explanation. 

All circumferentors (or miners compass) are not graduated 
alike. In all cases, 360° stands at the north point, and 180° 
at the south, but some are figured toward the right hand, from 
the north point, (which we call a right hand compass,) and 
others toward the left hand, so that a “right hand compass” 


130 


THE PRACTICAL MINERS’ 


has 90° at the east point, and a “left hand compass” has 90° 
at the west point. This diversity of graduation has often 
caused much perplexity and confusion among surveyors. 
The following table is contrived to suit both sorts of instru¬ 
ments, and is so plainly arranged and marked, as to require 
but little explanation. It must be specially regarded, that the 
table has been constructed upon the consideration that the eye 
of the surveyor has been applied to the south sight or vane 
standing against 180°; this must be invariably the case— 
hence, the north sight must always take the lead, and the 
young practitioner may here be told that in surveying a level 
and making double, or fore and back drafts, at every station, 
that although his eye must be placed at the north sight, 
necessarily, for the back observation, yet, as the compass has 
not been turned, the needle will stand to the true degree for 
the record, and no confusion or liability to error can occur. 

In converting an underground survey, or any other, from 
angles into bearings, it is obviously our first object to know 
the graduation of the instrument by which the work has 
been performed; and if it has been a “right hand compass,” 
and the first draft was on 167°, the bearing would be 13° 
west of south, but if it was done by a “ left hand compass,” 
the bearing would be 13° east of south. The only thing 
where a liability to error at all exists in obtaining the bearings 
by inspection from this table, and where caution is required, 
is in applying the fractions of degrees when they occur in the 
drafts; on these occasions, observe that when the angle and 
bearing progress alike, as in ail the left hand side of the 
column, then the fraction must be added to the whole number 
of the bearing, but otherwise, as in the right hand side, the 
fraction must be deducted from the whole number. Lastly, 

the following desirable proof may be resorted to:_If the 

course has been correctly converted, the degree and bearing 
added together or subtracted from each other, will make one 
of the following numbers : 0, 90, 180, 270, 360, and this may¬ 
be done almost at a glance after the survey has been con¬ 
verted into bearings. 


OWN BOOK AND GUIDE. 


131 


T A B L E 

For converting angles into bearings. 


Rt. Hd. Com. 

W. of N. 

Rt. Hd. Com. 

N. of W. 

Rt. Hd. Com. 

S. of W. 

Rt. Hd. Com. W.or S. 

Lt. Hd. Com 

K. of N. 

Lt. Hd. Com. 

N. of E. 

Lt. Hd. Com. 

S. of E. 

Lt. Hd. Com. E. of S. 

Angle. 

Bearing. 

Angle. 

Bearing. 

Angle. 

Bearing. 

Angle. 

Bearing. 

1 is 

1 

46 is 

44 

91 is 

1 

136 

is 44 

2 

2 

47 

43 

92 

2 

137 

43 

a 

3 

48 

42 

93 

3 

138 

42 

4 

4 

49 

41 

94 

4 

139 

41 

5 

5 

50 

40 

95 

5 

140 

. 40 

6 

6 

51 

39 

96 

6 

141 

39 

7 

7 

52 

38 

97 

7 

142 

38 

8 

8 

53 

37 

98 

8 

143 

37 

9 

9 

54 

36 

99 

9 

144 

36 

10 

10 

55 

35 

100 

10 

145 

35 

11 

11 

56 

34 

101 

11 

146 

34 

12 

12 

57 

33 

102 

12 

147 

33 

13 

13 

58 

32 

103 

13 

148 

32 

14 

14 

59 

31 

104 

14 

149 

31 

15 

15 

60 

30 

105 

15 

150 

30 

16 

16 

61 

29 

106 

16 

151 

29 

17 

17 

62 

28 

107 

17 

152 

28 

18 

18 

63 

27 

108 

18 

153 

27 

19 

19 

64 

26 

109 

19 

154 

26 

20 

20 

65 

25 

110 

20 

155 

25 

21 

21 

66 

24 

111 

21 

156 

24 

22 

22 

67 

23 

112 

22 

157 

23 

23 

23 

68 

22 

113 

23 

153 

22 

24 

24 

69 

21 

114 

24 

159 

21 

25 

25 

70 

20 

115 

25 

160 

20 

26 

26 

71 

19 

116 

26 

161 

19 

27 

27 

72 

18 

117 

27 

162 

18 

28 

28 

73 

17 

118 

28 

163 

17 

29 

29 

74 

16 

119 

29 

164 

16 

30 

30 

75 

15 

120 

30 

165 

15 

31 

31 

76 

14 

121 

31 

166 

14 

32 

32 

77 

13 

122 

32 

167 

13 

33 

33 

78 

12 

123 

33 

163 

12 

34 

34 

79 

11 

124 

34 

169 

11 

35 

35 

80 

10 

125 

35 

170 

10 

36 

36 

81 

9 

126 

36 

171 

9 

37 

37 

82 

8 

127 

37 

172 

8 

38 

38 

83 

7 

128 

38 

173 

7 

39 

39 

84 

6 

129 

39 

174 

6 

40 

40 

85 

5 

130 

40 

175 

5 

41 

41 

86 

4 

131 

41 

176 

4 

42 

42 

87 

3 

132 

42 

177 

3 1 

43 

43 

88 

2 

133 

43 

178 

2 

44 

44 

89 

1 

134 

44 

179 

1 

45 

45 

n1 /R. H.C.W. 
90 Ut.H.C.F,. 

] 135 

s 

45 

180 

South. 






























132 


THE PRACTICAL MINERS’ 


table 

For converting angles into bearings. 


Rt. Hd. Com. E. of S 
Lt. Hd. Com. W. of 8 

• Rt. Hd. Com. S of E. 

. | Rt. Hd. Com . S. of W. 

Angle 

Bearing 

. Angle 

Bearing. 

1 181 

is 1 

226 

is 44 

182 

2 

227 

43 

183 

3 

228 

42 

184 

4 

229 

41 

185 

5 

230 

40 

186 

6 

231 

39 

1&7 

7 

232 

38 

188 

8 

233 

37 

18.9 

9 

234 

36 

190 

10 

235 

35 

191 

11 

236 

34 

192 

12 

237 

33 

i 193 

13 

238 

32 

194 

14 

239 

31 

195 

15 

240 

30 

1 196 

16 

241 

29 

197 

17 

242 

28 

198 

18 

243 

27 

199 

19 

244 

26 

200 

20 

245 

25 

201 

21 

246 

24 

202 

22 

247 

23 

203 

23 

248 

22 

204 

24 I 

249 

21 

| 205 

25 

250 

20 

206 

26 

251 

19 

207 

27 

252 

18 

208 

28 

253 

17 

209 

29 

254 

16 

210 

30 

255 

15 

211 

31 

256 

14 

1 212 

82 

257 

13 

213 

33 

258 

12 

214 

34 

259 

11 

215 

35 

260 

10 

216 

36 

261 

9 

217 

37 

262 

8 

218 

38 

263 • 

7 

219 

39 

264 

6 

220 

40 

265 

5 

! 221 

41 

266 

4 

222 

42 

267 

3 

223 

43 

268 

2 

224 

44 

269 

1 

225 


270 | 

R.H.C.E. 1 
L.H.C.W. j 


Rt. Hd. 

Com. N of E 

Rt. Hd. Com. 

E. of N. 

Lt. Hd. 

Com. N. of \\ 

'. Lt. Hd. Com. 

W. of N. 

Angle 

Bearing 

. Angle. 

Bearing. 

271 

is 1 

316 is 

44 

272 

2 

317 

43 

273 

3 

318 

42 

274 

4 

319 

41 

275 

5 

320 

40 

276 

6 

321 

39 

277 

7 

322 

38 

278 

8 

323 

37 

279 

9 

324 

36 

280 

10 

325 

35 | 

281 

11 

326 

34 

282 

12 

327 

33 

283 

13 

328 

32 

284 

14 

329 

31 

285 

15 

330 

30 

286 

16 

331 

29 

287 

17 

332 

28 

288 

18 

333 

27 

289 

19 

334 

26 

290 

20 

335 

25 

291 

21 

336 

24 

292 

22 

337 

23 

293 

23 

338 

22 

294 

24 

339 

21 

295 

25 

340 

20 

296 

26 

311 

19 

297 

27 

342 

18 

298 

28 

343 

17 

299 

29 | 

344 

16 

300 

30 

345 

15 

301 

31 

346 

14 

302 

32 

347 

13 

303 

33 

348 

12 

304 

34 

349 

11 

305 

35 

350 

10 

306 

36 

351 

9 

307 

37 

352 

8 

308 

38 

353 

7 1 

309 

39 

354 

6 

310 

10 

355 

5 

311 

41 

356 

4 

312 

42 

357 

3 

313 

43 

358 

2 

314 

44 

359 

1 

315 

45 

360 North. 

















































OWN BOOK AND GUIDE. 


133 


Application of the Converting Table. 

Suppose the needle stood at 246+, what is the bearing? 

Ans. $ a right-hand compass 23+ South of E. 

£ By a left-hand compass 23+ South of W. 

It may be remarked that the table is equally applicable for 
changing bearings into angles if required; for example:—An 
observation was made with a right-hand compass, and the 
bearing found to be 27° 17' E. of N., at what degree did the 
needle point ? 

Ans. 332° 43', and if proof is required it will be seen that 
the sum of these degrees and minutes is 360°. 


EXAMPLE. 


Convert the following angles taken with a left-hand com¬ 
pass into bearings:— 


210+ 

, 176 

i°, 305J°, 

28*°, 107*,° 

97+? 


Operation. 


Proof. 


210+ 

is 30+ 

W. of S. 

210+—30+ 

II 

1— > 

00 

0 

176* 

3* 

E. of S. 

176* 

+ 3* 

= 180 

305* 

35| 

N. of W. 

305| 

—35| 

=270 

28* 

28* 

E. of N. 

28* 

—28i 

= 0 

107* 

17* 

S. of E. 

107* 

-17£ 

— 90 

97* 

7f 

S. of E. 

97f 

- n 

= 90 

348 

12 

W. of N. 

348 

+12 

=360 


EXAMPLE. 

* 

Convert the following angles taken with a right-hand com¬ 
pass into bearings:— 

9? 45', 239° 25', 331° 12', 160° 58', 45° 6'? 


Operation. 

9° 45' is 9° 45 / W. of N. 
239 30 35 S. of E. 

331 28 48 E. of N. 

160 19 2 W.ofS. 

45 44 54 W. of N. 


Proof. 

90 45 / — 9° 45'= 0° 
239 25+30 35=270 
331 12 —|—28 48 =360 
160 58+19 2=180 

44 54+45 6= 90 


In practice it would not be necessary or convenient to state 
proofs—it is introduced here for the learners sake that he may be en¬ 
abled to insure certainty in this essential matter. 

6 # 






134 


THE PRACTICAL MINERS’ 


In pressing on our young mining friends the advantage of 
adopting a perfect system, we advise that in preparing a course 
of surveying for trigonometrical solution by changing the 
angles into bearings, care should be taken that all the drafts 
should be made either to exceed 45°, or that they should all 
stand below or at least not exceed that half quadrant. Our 
reason for being urgent on this matter is, that there may be a 
uniformity in placing the sides in the traverse table after the 
draft has been computed, and let it be particularly noticed that 
if the bearings are not suffered to exceed 45°, that the last ex¬ 
pression ol the bearing will signify the longest of the two 
sides; that is, suppose a draft taken underground was 287£°, 
measuring 4.5 feet 8 inches, now looking at the 44 converting 
table we see that if this draft was taken with a 44 left-hand 
compass” that the bearing is 17£° north of west, (or N. of 
W.) and the two sides will be found by computation-to be 13 
feet 7 inches and 43 feet 7 inches. Query, into what columns 
respectively must these numbers be placed ? As the bearing 
was north of west, and our system states that 44 the last ex¬ 
pression of the bearing will signify the longest of the two 
sides,” consequently the longest side (43 feet 7 inches) must 
be placed in the 44 west ” column, and 13 feet 7 inches in the 
north column. If this order is followed up, it will render the 
working of traverse, (which is the most important operation 
in mine surveying,) a plain, pleasing, satisfactory exercise. It 
is our desire on this subject to bring forward every thing like¬ 
ly to promote the advancement of the young mining officer in 
this paramount branch of his profession, and therefore give 
him to understand that in traversing there must be a regular 
course from beginning to end. We shall make ourselves un- 
deistood in this matter by taking a case where a person makes 
a survey for the purpose of ascertaining the length and bear¬ 
ing of a level driven in an east and west lode, and for some 
convenient purpose, he begins his surveying at some point 
about the middle of the level, and surveys from thence to the 
eastern end; he then returns to the station or start at the mid- 


OWN BOOK AND GUIDE. 


135 


die of the level and surveys on to the western end and thus 
completes the survey. Now if he was to proceed to work the 
traverse from his surveying book in this state, his results would 
appear as if his level was almost without length or bearing, as 
his eastings would be balanced by his westings, &.c. In or¬ 
der to go systematically to work in this case, his first opera¬ 
tion must be to reverse the order of one or the other of the 
surveyings; that is, if he pleases to let the first remain, which 
is the eastern surveying, and would accommodate the western 
part to suit the other, he must alter or reverse all the drafts, by 
converting (say) 16° south of west, into 16° north of east, 
and so of all the rest. In winding up this course of instruc¬ 
tion, we will take a short survey and go through with it at 
length and the student may accompany us if he pleases, for 
we are still of the same opinion as we always have been that 
practical teaching is the best. 

EXAMPLE. 

it is required to sink a vertical shaft on the end of a level 
and the surveyings from the bottom of an old downright shaft 
are as follows, surveyed with a right-hand compass ?” 

fath. ft. in. 

No. 1. 356£° Length 18 3 0 

2. 84£° 12 1 6 

3. 98° 15 4 0 

4. A winze 322°, underlay 25^°, inclined 

length 11 2 

5. 107£° Length 25 5 6 end. 

This is the underground work, and our first operation is to 

find out the underlay of the winze in order that it may stand 
as a common draft in the survey. 

OPERATION. 

The underlay or angle made by the dip of the winze and a 
vertical line, being 25^ degrees, we find it standing in the first 
table against 2 feet 7 inches, showing that every fathom of the 
winze gives a base of 2 feet 7 inches, and the length of the 
winze being 11 fathom 2 feet, we multiply 


136 


THE PRACTICAL MINERS' 


ft. 

i)2 


in. 

7 

11.2 


44 5 

10 


4 5 3 

Here we find the base of the winze to be 4 fath. 5 ft. 3 in. 

The next thing is to refer to the converting table to reduce 
the drafts into bearings, taking special notice that the work 
was done with a right-hand compass. 

We therefore find that No. 1. 356£° is 3|° E. of N. 

2. 84£ 5 £ N. of E. 

3. 98 8 S. of W. 

Winze 4. 322 28 E. of N. 

5. 107f 17f S. of E. 

Our work is now prepared for entry in the traverse table as 
data for trigonometrical computation. 


1 No. 

Angles and Lines. 

Trigonometrical Results. 

Draft. 

! Bearings. 

Lengths. 

East 

West 

North 

South 

1 

3£° E of N. 

fath. 

18 

ft. 

3 

in. 

0 





2 

5~k 

N. of E 

12 

1 

6 





3 

8 

S. of W 

15 

4 

0 





4 

28 

E. of N. 

4 

5 

3 





! 5 

17f 

S. of E. 

25 

5 

6 






The above is the table with the bearings and lengths of the 
drafts entered in order for receiving the trigonometrical results 
in their proper and respective columns, and that every thing 
may be clear to the learner we shall let this table remain as it 
is, and make a similar one in which the computations are en¬ 
tered, and proceed to take out the tabular numbers from the 
first mathematical table and multiply them by their respective 
lengths. 






























OWN BOOK AND GUIDE. 


137 


First Draft. 

ft. m. 

ft. in. 

Z3|° Tabular 0 4.7 Tabular 5 11.85* 

6 

6 

2 2.2 

35 11.10 

3 

3 

6 6.6 

107 9.30 

2.3 

2 11.92 

6 8.9 Eastings. 

110 9.2 Northing. 

Now the sides of the triangle formed 

by the first draft are 

ready to be transferred to the east and 

north columns of the 

traverse table. 

Second Draft... 

ft. in. 

ft. in. 

L 5 h 0 Tabular 0 6.9 Tabular 5 11.67 

12i 

m 

6 10.8 

71 7.92 

1.7 

1 11.42 

7 0.5 Northing. 

73 7.3 Easting. 


When the bearing does not diverge from the cardinal point 
there is but little difference between the length of the hy- 


pothenuse and the longest of the legs, as in the right hand 

sides of the above two drafts. 



Third Draft. 



ft. in. 

ft. 

in. 

Z8° Tabular 8 10.02 Tabular 

5 

11.3 

8 


8 

6 8.16 

47 

6.4 

2 


2 

13 4.32 

95 

0.8 

3.31 

1 

11.8 

13 1.0 Southing. 

93 

1.0 Westing. 






























138 


THE PRACTICAL MINERS’ 


The length of the draft being 15 fathoms 4 feet, we have 
multiplfed by 16, and deducted ^ as the shortest method. 


Fourth Draft or Base of Winze. 


ft. in. in. 

ft. in. in. 

/28°Tab.2 9.8or31.8 

Tab. 5 3.6 or 63.6 

5 

5 

169.0 

318.0 

4.2 

7.9 

12)164.8 

12)310.1 

13.8.8 Easting. 25.10.1 North’g. 

In the above, it will be 

seen that we have thrown the tabu- 

lar lengths into inches and 

parts, and the practitioner will find 

this, in general, the easiest way of calculating. 

Fifth Draft. 

ft. in. in. 

ft. in. in. 

Z 17jf Tab. 1 10.0 or 22.0 

Tab. 5 8.6 or 68.6 Easting. 

26 

26 

132 

411.6 

44 

1372 

572.0 

1783.6 

1.8 

5.7 

12)570.2 

12)17779 


47.6.2 South’g. 148.1.9 Easting. 


















OWN BOOK AND GUIDE. 


139 


Now the computations are ready for entry in the following 
table: 


No. 

Angles and Lines. 

1 

Tngnometrical Results. 

Draft. 

Bearings. 

Lengths. 

East. 

West. 

North. 

So uth. 

1 

2 

3 

4 

5 

3»° E. of N. 
5| N.ofE. 

8 S. of W. 
28 E. of N. 
17? S. of E. 

fath. ft. in. 

18 3 0 

12 1 6 

15 4 0 

4 5 3 

25 5 6 

ft. in. 

6 8.9 
73 7.3 

ft. in. 

ft. in. 

110 9.2 
70.5 

ft. in. 



93 1.0 

13 1.0 

13 8.8 
148 1.9 

25 10.1 


47 6.2 

‘ 




242 2.9 
93 1.0 

93 1.0 

143 7.8 
60 7.2 

60 7.2 

149 1.9 Easti’g. 

83 0.6 North ’g 


Now we might proceed to lay down the position or place 
of our new vertical shaft at the surface without any further 
operation. For by measuring off from the centre of the old 
shaft, at surface, 149 feet 2 inches, due east, and from the end 
of that line measuring 83 feet due north, would bring us ex¬ 
actly over the end of the fifth or last draft, where the shaft is 
to come down, but we would work out the direct length and 
bearing also, as before described, and apply it. 

PROBLEM. 

We will suppose that at a certain copper mine a new 
vertical shaft was commenced which is intended to intersect 
the main lode at the depth of 100 fathoms below the adit 
level, which is about 40 fathoms from surface, in the vicinity 
of the new shaft. From a point in this level, a drift or cross¬ 
cut has been begun, and designed to be driven in a direct line 
to the centre of the new shaft, and from thence to rise against 
it, if necessary, and the aim and object of the survey is to 
ascertain the exact length and bearing of the said cross-cut, 
as every proper means have been adopted to certify that it has 
been commenced at the nearest point to the shaft. 

The following is the whole course of surveying in its most 
simplified form, with the irregular surface lines reduced to 












































140 


THE PRACTICAL MINERS* 


horizontal measure, the angle of every draft converted into 
bearing, and the whole given in complete order for working 
the traverse without any preliminary preparation. The draft 
standing on the top of 934 feet is from the centre of the new 
shaft at surface to a line hung in the old engine shaft, which 
is also vertical to the adit, and the next draft is taken from 
that line in the adit and continued to the end of the 34th 
draft, through the same level where the cross-cut commences. 
It is also required to furnish the bearing of the lode from the 
3d to the 34th draft inclusive. 

REMARKS. 

As this course of surveying has been rendered so plain, 
there appears to be no occasion to introduce a double entry 
of it, as the field and underground work is sufficiently mani¬ 
fest in the first three columns of the following table, in com¬ 
bination with the trigonometrical operation. It may be satis¬ 
factory to the student to be informed that this work has been 
accomplished and proved to be perfectly correct. 


OWN BOOK AND GUIDE 


141 


COMPUTATION. 


No. 

Angles and Lines. 

Tri 

Drafts. 

Bearings. 

Lengths. 

East. 

From new shaft to 






engine shaft. 

ft. 

in. 

ft. 

in. 


14° 18' S. of W. 

934 

0 



1 

13| 

S. of E. 

30 

0 

29 

0.7 1 

2 

4f 

E. of S. 

30 

6 

2 

6.3 


On course of lode. 





3 

5i° 

S. of E. 

28 

6 

28 

4.5 

4 

4 

N. of E. 

42 

6 

42 

4 7 

5 

16 

S. of E. 

30 

8 

29 

5.8 

6 

2 I 

S. of E. 

32 

0 

31 

117 

7 

18* 

S. of E. 

29 

2 

27 

8.9 

8 

4 i 

S. of E. 

, 18 

0 

17 

11.5 

9 

Si 

N. of E. 

36 

0 

35 

10.2 

10 

13 

S. of E. 

17 

0 

16 

6 8 

11 

19 = 

S. of E. 

26 

6 

24 

11.2 

12 

14 

S. of E. 

22 

7 

21 

11.0 

13 

15 

S. of E. 

36 

3 

35 

0.1 

14 

1 

S. of E. 

46 

6 

46 

5.9 

15 

17 

N. of E. 

41 

3 

39 

5.4 

16 

4 

N. of E. 

11 

2 

11 

1 7 

17 

21| 

N. of E. 

12 

8 

11 

9.4 

18 

1 

N. of E. 

27 

0 

27 

0.0 

19 

2 

N. of E 

38 

8 

38 

7.7 

20 

1 

S. of E. 

18 

0 

18 

0.0 

21 

20 

S. of E. 

12 

6 

11 

8.9 

22 

7 

S. of E. 

11 

6 

11 

5.0 

23 

1 

S. of E. 

25 

8 

25 

8.0 

24 

4 

N. of E. 

31 

6 

31 

5.1 

25 

13 

S. of E. 

34 

6 

33 

7.4 

26 

1 

N of E. 

18 

8 

18 

8.0 

27 

5 

N. of E. 

28 

0 

27 

10.7 

28 

8 

S. of E. 

65 

0 

64 

4 4 

29 

2 

S. of E. 

36 

6 

36 

0.4 

30 

5 

S. of E. 

18 

0 

17 

11.2 

31 


N. of E 

24 

8 

24 

6.0 

32 

l 

N. of E. 

12 

3 

12 

3.0 

33 

18 

N. of E. 

29 

6 

28 

0.7 

34 

12 

N. of E. 

20 

1 

19 

7.8 






899 

6.1 






Westir 


Trigonometrical Results. 


West. 1 North. 

ft. in. 
905 0.7 

ft. in. 







2 11.6 









2 2.4 






. 

. 


12 0.7 

0 9.3 1 



4 7.7 

0 5 7 

1 4.2 


-- 








2 2.3 



0 3.9 

2 5.3 








2 9 5 

0 2.6 
9 1.4 

4 2.1 





905 0.7 
899 6.1 

45 8.7 


South. 

ft. 

in. 

230 

8.3 

7 

1.6 

30 

4.8 

2 

8.8 

8 

5.4 

1 

4 7 

9 

1 6 

1 

4.0 

3 

9 9 

8 

11.4 

5 

5.6 

9 

4.6 

0 

9.8 


0 3.8 
4 3.4 
1 4.8 
0 5.3 


7 9.1 


9 0.6 
1 3.3 
1 68 


345 9.6 
45 8.7 


Westing 5 4.6 South’g 300 1 9 






















































































142 


the practical miners 


the,, by the foregoing method of proceeding, the required 

answers will be found as follows 

Length of cross-cut from adit to centre of shaft 300 feet 2 
inches. 

Bearing of cross-cut 1° 2' west of north. 

Bearing ot lode from third to thirty-fourth draft inclusive, 
south of east. 

PROBLEM. 

^ lode was opened on the back by costeening in several 
places, and its course by compass found to be 104° south of 
east, but this was on the ascent of a steep hill whose angle of 
elevatton was 16*°, and the lode „ nderlaying northerl ° 3 J 
m a perpendicular fathom. ^ 

whm’7 y ' i7T U the true bearin ° 0r course of the lode, and 

600 faIh U d 7 the am ° Unt ° f err ° r carr y* n S on the line 

bad- o the? 7 measure ) s “PP™"g the run of the 

stead ofte t 7 aSC , ent ,md b6en taken ’ ^ in- 

stead ot the true horizontal course ? 

OPERATION. 

We find in the first table that 16*° of elevation gives 1 foot 
8.45 inches perpendicular, and 5 feet 9.04 inches base for the 
corresponding sides of the triangle. 

ft. fa 

Hence if 6 perp. gives 3 underlay, what will 1 8.45 give? 

12 19 


72 


36 


20.45 

36 


or , , 72)736.20(10.2 

Showing that the underlay of the lode carries the line 104 
inches further north than the line taken at the surface (or bear! 
mg) on every horizontal line of 5 feet 9.04 inches. Therefore 
we have the two sides of a right-angled triangle 5 feet 9 04 

willlelh ‘ nCheSa “ d thean ? le °PP° si ‘e the shortest side 
Will be the amount ol the angle of error. 




143 


OWN BOOK 

AND GUIDE. 


ft. in. 

in. 

ft. 

5 9.04 : 

10.2 : : 

6 

12 


12 

69.04 


72 

10.2 in. 


69.04)734.4(10.63 

By inspection of the second table we find the nearest next less 
angle standing opposite this number (10.63 inches) is 8° 15', 
giving 10.44 inches; and as the difference between this and the 
next greater (8^) is .32, and the difference between 10.63 
inches and 10 44 inches is .19, we say 

As .32 is to .19 so is 15' — 9' 

And 9' added to 8° 15' gives 8° 24' for the angle of error, and 
by deducting this angle of error (if it may so be called) from the 
course of the lode on the inclined surface (10£ south of east) 
we have 2° 6' south of east for the true bearing of the lode, 
and as the error is 10.64 inches in a horizontal fathom, this 
number multiplied by 600 gives 6384.00 inches, or 88| fathoms 
too far south on a line of 600 fathoms. 

PROBLEM. 

Suppose a 20 fathom level, driving on an east and west lode 
underlaying north, a winze has been commenced bearing due 
north, and it is determined to pitch a rise against it in the 40 
fathom level (the 30 fathom level not having been driven far 
enough east to rise from.) The following is a statement of 
the surveying from the middle of the above winze, in the twen¬ 
ty, through the level west towards another winze sunk to the 
30 fathom level. 

No ft. in. No. ft- in. 

1 2824° 59 10 3 264^° 33 4 

2 286° 61 8 4 260^° 77 3 

This brings us to the brace of the winze communicating 

with the 30 fathom level, which we may call No. 5, its dia¬ 
gonal length 65 feet, underlay 22£ degrees, bearing 9-£° east 
of north. From the foot of this winze in the 30, the survey¬ 
ing is continued westerly to another winze communicating 
with the 40 fathom level, viz: 





144 


THE PRACTICAL MINERS* 


No. 

6 

7 

8 


272£° 

ft. 

60 

256° 

52 

287i° 

45 


in. 

9 

0 

8 


W .® " ow arrive the brace of the winze to the 40, which we 
call No. 9, length 70 feet 6 inches, underlay 3 1 bearing 4° 
v .st of north. From the bottom of this winze in the 40, the 
course turns easterly and is continued in that direction, viz • 

ft. in . ’ 


No. 

10 

11 

12 


83° 

77° 

104i° 


ft. in. 

85 4 
28 5 
76 0 


No. 

13 

14 

15 


90° 

92^o 

99° 


ft. in. 

77 6 
23 8 
107 2 


At the end of this 15th draft we place an assumed mark in the 
back of the 40 fathom level. 

Question. It is required to know how far we must measure 
east or west from this mark in order to arrive at the exact 
pomt for rising against the winze sinking from the 20 fathom 
lev 1 also what will be the average underlay at that place, and 

what will be the length of the winze from the 20 to the 40 fa- 
thorn level ? 

COMPUTATION—(Surveyed with a left-hand compass.) 


No. 


Angles and Lines. 


Draft. Degree 


1 

2 

3 

4 

5 

6 

7 

8 
9 

10 

11 

12 

13 

14 

15 


2821 

286 

264| 

260i 

winze 

2721 

256 

2871 

winze 

83 

77 

1041 

90 

92 

99 


Bearing. 

Length. 

121 

\ N. of W. 

ft. 

59 

in. 

10 

16 

N.o/W. 

61 

8 

6J 

; S. of W. 

33 

4 

91 

; S. of W. 

77 

3 

H 

E. of N. 

24 

10 


N. of W. 

60 

9 

14 

S. of W 

52 

0 

171 

N. of W. 

45 

8 

4 

W. of N 

36 

10 

7 

N. of E. 

85 

4 

13 

N. of E. 

28 

5 

14i 

S. of E. 

76 

0 

East 

77 

6 

2* 

S. of E 

23 

8 

9 

S. of E. 

107 

2 



Easing 12 7 North’g 58 7 










































































OWN BOOK AND GUIDE 


145 


Now we discover, by the foregoing calculation, that our as¬ 
sumed mark in the 40 fathom level is 12 feet 7 inches too far 
east for the central point of the rise against the winze sinking 
from the 20, and which was the paramount object required. 

The first operation in working this problem is to find the 
base and perpendicular of the two winzes, numbers 5 and 9, 
and their respective bases from the operative lines in the above 
traverse. 

ft- in. ft. in. 

Winze No. 5, gave 24 10 base and 60 1 perpendicular. 

Winze No. 9, gave 36 10 base and 60 1 perpendicular. 

Now the vertical depth being 120 2, and the base or 
northing 60 feet 5 inches, we have thus the two sides of a 
right-angled triangle to find the hypothenuse and dip or angle 
of declination which on trial will be found— 

Hypothenuse, or length of winze, 134 feet. 
Angle, or underlay of winze, 26^ degrees. 

PROBLEM. 

Suppose a tunnel has been commenced at the foot of a hill, 
and is intended to be driven through it. The bearing from 
the above point, or the course of the tunnel is to be due east, 
and it is required to know the exact corresponding point on 
the other side of the hill, in order to set another company of 
men to drive a dead level to meet the drivings that are pro¬ 
gressing from the west side ? 

The length of the tunnel is also required ? 


Note. —As the last draft (reversed) is 9° N. of W. in order to be 
quite accurate, it will require us to measure 12 feet 9 inches back 
through the level to make good 12 feet 9 inches westing, and this will 
give 1 foot 10 inches more of base or northing, which added to 58 feet 
7 inches, the underlay shown by the column of northing will give the 
answer to the question, 60 feet 5 inches for the whole underlay. 




146 


THE PRACTICAL MINERS 


The following is the survey from the first point:— 


No. 1. 

Elevation 

14° 

Length 26 feet 

2 . 


12 * 

26 

3. 


11 

17 

4. 


18* 

90 

5. 


10 

60 

6 . 


71 

119 

7. 

Horizontal 

0 

29 

8 . 

Depression 


28 

9. 


16 

230 


Judging that we have now arrived somewhere near the level 
or horizontal plane of the start, or that our “depressions” 
have made good our “ elevations,” we place an assumed mark 
at the end of the last or ninth draft, and retire to work out 
our lines and angles by trigonometry. 

OPERATJOiV. 

Perp. Base, 
fath. ft. ft. in. ft. in. 

No. 1 . Elevation 14° length 4 2 tab. 1 5.4 5 9.9 

4* 4* 


5 9.6 

23 

3.6 

5.8 

1 

11.3 

6 3.4 

25 

2.9 


Thus we find the first draft gives a rise or elevation of 6 
feet 3.4 inches, and base or horizontal length 25 feet 2.9 in¬ 
ches, and proceeding in the same manner with all the drafts 
and finding the difference between the elevations and depres¬ 
sions, we shall obtain true data for correcting our assumed 
mark and replacing it in its proper position. 











OWN BOOK 

AND 

GUrDE. 



Elevation. 


Horizontal 


ft. 

in. 


ft. 

in. 

No. 

1 gives 6 

3.4 

and 

25 

2.9 

No. 

2 gives 5 

62 

and 

25 

4.9 

No. 

3 gives 3 

2.9 

and 

16 

8.3 

No. 4 gives 28 

6.0 

and 

85 

4.0 

No. 

5 gives 10 

5.0 

and 

59 

0.1 

No. 

6 gives 14 

8.5 

and 

118 

1.0 


68 

8.0 




No. 

7 gives 



29 

0.0 


Depression. 




No. 

8 gives 2 

8.2 

and 

27 

10.5 

No. 

9 gives 63 

3.8 

and 

220 

3.0 


66 

0.0 


606 

10.7 


Now as the depression are 2 feet 8 inches less than the 
elevation, it demonstrates that our assumed mark is 2 feet 8 
inches too high, and as the declination of the ground from 
the last draft eastward continues on the same angle of depres¬ 
sion of 16 degrees, we have perpendicular 2 feet 8 inches and 
angle 16° to find the corresponding hypothenuse and base— 
and by inspection of the second table we see that the “ tabu- 
lars ” opposite 16° are 1 foot 8.6 inches, and 6 feet 2.9 in¬ 
ches hypothenuse— 

Therefore, if 1 foot 8.6 inches gives 6 feet 2.9 inches, what 
will 2 feet 8 inches give? 

Which will be found to give 9 feet 8 inches of hypothe¬ 
nuse. 

And by the first table it will be found that 9 feet 8 inches 
of hypothenuse on an angle of 16° will give for the longest 
side or base 9 feet 4 inches. 











148 


THE PRACTICAL MINERS’ 


Adjustment.. 

By removing' the assumed mark, 9 feet 8 inches, due east, on 
the slope, we fix on the exact spot for commencing the 
eastern end of the tunnel, and we need hardly observe that 
the two extreme marks mean the bottom or floor of the tunnel. 

Then by adding the base, 9 feet 4 inches, made by the cor¬ 
rections to the sum of the horizontals, 606 feet 10.7 inches, 
we have just 616 feet 3 inches for the length of the tunnel. 


PROBLEM. 


It is intended to sink a shaft on the end of a level driven 


from old shaft, and the following is the survey from the 
centre of the old shaft to the end of the level, viz : 


No. 




ft. 

in. 

1 

3° 

W. of 

N. 

45 

0 

2 

n 

N. of 

E. 

24 

6 

3 

84 

N. of' 

E. 

18 

0 

4 


East 


49 

1 

5 

12 

S. of 

E. 

30 

0 


No. ft. in. 

6 6|° S. of E. 37 0 

7 15 S. of E. 16 5 

8 5 N. of E. 21 9 

9 12^ N. of E. 14 7 

10 9 W. ofN. 28 0 


As profound accuracy is required in this case, (it being in¬ 
tended to facilitate the work by rising against the new shaft 
from the end of the level,) a reverse or proof course of sur¬ 
veying has been made from the end back to the centre of the 
old shaft, viz: 


S T 0. 



ft. 

in. 

1 

0 

OO 

E. of S. 

26 

10 

2 

11 

S. of VV. 

15 

0 

3 

4J 

S. of W. 

19 

6 

4 

13£ 

N. of W. 

20 

0 

5 

9* 

N. of W. 

52 

3 


N °- ft. in. 

6 li S. of VV. 44 0 

7 7 S. of W. 26 0 

8 9f S. of W. 22 H 

9 E. of S. 43 10 


Note —Should it be required to put down vertical shafts on the 
tunnel, the foregoing computations reveal what their depths would be 
respectively at all parts ol the tunnel, and the deepest shaft would be 
11 fathoms 2 feet 8 inches at the end of the sixth draft, and 55 fathoms 
from the western mouth of the tunnel. 









OWN BOOK AND GUIDE. 


149 


It is now required to know if there is an exact agreement 
between these two surveys, or fore and back surveyings, (or 
what is the difference between them,) and if so, what is the 
length and bearing from the centre of old shaft, at the sur¬ 
face, to the point exactly over the end of the level where the 
centre of the new shaft must be fixed ? 

OPERATION. 

From Old Shaft to Eastern End. 


No. 


Drafts. 


No. 

Angles and Lines. 

T) 

Drafts. 

Bearings 

Leng 

ths. 

East. 




ft. 

in. 

1 ft. 

in. 

1 

3° 

W. of N. 

45 

0 



2 


N. of E. 

24 

6 

! 24 

3.7 

3 


N. of E. 

18 

0 

17 

9.6 

4 


East. 

49 

1 I 

1 49 

1.0 

5 

12 

S. of E. 

30 

0 

29 

4.1 

6 

6| 

S. of E. 

27 

0 

26 

9.8 

7 

15 

S. of E. 

16 

5 

15 

10.3 

8 

5 

N. of E. 

21 

o 1 

20 

11.0 

9 

121 

N. of E. 

14 

7 ! 

14 

3.0 

10 

9 

W. of N. 1 

28 

0 






198 
| 6 

Easting 191 

4.5 

8.8 

7.7 


Trigonometrical Results. 


West. 

North. 

ft. in. 
2 4.2 

ft. in. 
44 11.2 
3 1.1 

2 7.9 










1 10.0 
3 1.1 

27 7.9 


4 4.6 

6 8.8 

83 3.2 

13 7.9 

Northing 69 7.3 


South. 


ft. in. 
. 


6 2.8 

3 2.1 

4 3.0 


From Eastern End to Old Shaft. 


Angles and Lines. 


Bearings. 


8 ¥ 

n 

n 

13* 

n 

7 

n 

n 


> s. 
s. 
s. 

N. 

N. 

S. 

s. 

s. 

E. 


of E. 
of W. 
of W. 
of W. 
of W. 
of W. 
of W. 
of W. 
of S. 


ft. in. 
26 10 
15 0 

19 6 

20 0 
52 3 
44 0 
26 0 
22 8 
43 10 


Trigonometrical Results. 

East. 

West. 

North. 

South. 

ft. in. 

3 11.6 

ft. in. 

ft. in. 

ft. in. 
26 6.5 

2 10.3 

1 7.4 

14 8.7 

19 5 2 

19 5.6 

51 6.5 

43 11.9 
25 9.7 

22 4.1 





4 7.0 

8 7.5 




0 11.5 
3 2.0 

3 10.1 
43 9.6 





1 8.6 




5 8.2 

197 3.7 

5 8 2 

13 2.5 

82 9.4 

13 2.5 

Westi’g 

191 7.5 

Southi’g 

69 6.9 


7 


































































































150 


THE PRACTICAL MINERS’ 


Now we find that as the westing and southing of the back 
surveying corresponds with the easting and northing of the 
direct surveying to the fraction of an inch, it amounts to a 
mathematical demonstration of the perfection of the under¬ 
ground survey. It now only remains for us to obtain the 
hypothenuse and angle opposite the base of the two given 
sides ot the triangle formed by the easting 191 feet 7f inches, 
and northing 69 feet 7 inches, which will be found to give— 
Length, (from centre’ of old shaft to point over end,) 203 
feet 11^ inches. 

Bearing, 20 degrees north of east. 


FLANS AND SECTIONS OF MINES. 

Persons who have not had practical experience in mining 
often acknowledge that they find great difficulty in compre¬ 
hending the plans and sections of a mine, or of having a true 
idea of the workings from an inspection of the drawings.— 
0 his obscurity may be occasioned from an imperfection in the 
plans; for if they have been executed under a good system, 
it can hardly fail to exhibit clearly every part of the workings, 
and indeed, if the diagrams have not been executed perfectly 
and according to rule and order, even miners themselves can¬ 
not comprehend them. It requires four distinct mathematical 
or geometrical drawings to represent a mine, which we will 
biiefly notice under each head; and we may observe, as we 


N. B.— After this length and bearing has been applied at the surface, 
and the point fixed for the centre of the new shaft, an infallible and 
desirable proof that this last and important work has been done cor¬ 
rectly, may be obtained by availing ourselves of the ready means placed 
within our reach by the cardinal points or sides of the great triangle. 
Thus, by measuring ofif from the centre of old shaft 191 feet 7f inches, 
due east, and then from the end of that line 69 feet 7 inches, due north,' 
the end will fall exactly on the point fixed at the end of the line 203 
feet Hi inches on the bearings of 20 degrees north of east, if the whole 
has been done correctly. 





OWN BOOK AND GUIDE. 


151 


pass on, that the common cause of people in general not un¬ 
derstanding the plans is because they expect to know too much 
at first sight. 

With this introduction we proceed to state that the set of 
drawings may be described thus :— 

1. Ground plan. 

2. Horizontal or working plan. 

3. Longitudinal section. 

4. Transverse section. 

And taking them in order as we will place them we begin 
thus:— 

(1.) The Ground Plan. 

This plan may be on a scale of three or four chains to an 
inch, and every lessor or land-owners bounds should be dis¬ 
tinctly marked on this map. On this map it should be parti¬ 
cularly pointed out if there is any intervening ground, that 
has not been legally granted, so that proper applications may 
be made in due time and not leave it until the workings have 
been commenced, and good discoveries of coal or other min¬ 
erals made and then this land-owner, taking advantage of the 
neglect or oversight, demands an unreasonable premium for 
breaking the barrier under his land or prohibits the drifting 
one inch further under it. 

(2.) Horizontal or Working Plan. 

This is the miners’ plan, his chart, his guide, his right hand, 
and whoever attempts to conduct the operations of a mine 
without a perfect working plan and a perfect knowledge of it, 
is unfit for his office. The very circumstance of his suppos¬ 
ing himself capable of doing so without it is a certain proof 
of his ignorance. This plan gives what surveyors call a bird 
eye view of the mine. Or let us suppose that the ground is 
transparent and by walking over the surface we could look 
down and distinctly see all the underground workings. If 
this part of mining operations had been strictly attended to, 
the loss of life and property by unexpectedly holeing into old 


152 


THE PRACTICAL MINERS’ 


workings would not have been as great as it has been. A per¬ 
son who never saw a mine will understand from a view of this 
plan that he could distinguish the course of all the levels and 
upsets in all their turns and windings, and will have a correct 
view of all the underground work. On addressing myself to 
the miner as regards the best method of constructing and keep- 
ing up a working plan, I will endeavor to explain which, in my 
opinion, is the best, at least I have found it so after many years 
experience. Let the scale be five fathoms to an inch; before 
you begin to lay down any part of the workings, draw faint 
lines over your sheet of drawing paper at right angles. These 
lines will be your cardinal points. This plan proved correct 
and well kept up becomes invaluable to all mining agents. 

(3.) Longitudinal Sections. 

The only real benefit of this section to the miners is, that 
it may be so contrived to show the dip or inclination or decli¬ 
nation of the courses of ore or minerals of any kind, and this 
circumstance he may turn greatly to his advantage in working 
a mine, especially in working a copper mine, or a gold or a 
lead mine. For example, suppose in driving a fifty fathom le¬ 
vel going east, we cut into a course of ore and it continued 25 
fathoms in length; let these two points of the coming in and 
going out of the course of ore be correctly marked in this 50 
fathom level of this section. In the next level below the same 
course of ore is struck four fathoms further west than it was 
in the 50, and the course of ore at this level proved to be 28 
fathoms long. Let these points also be marked on this sec¬ 
tion. The agent or manager is now in possession of a clue 
whereby he may form a correct idea at what place the course 
of ore will be found in the level, below which will be still 
deeper, and also at what point it will fail in driving east, which 
will better qualify him for setting contract work with the help 
of this section than if he had no such, guide. 

(4.) Transverse Section. 

Here the view of the workings are exhibited to the mining 
agent who will see the workings, and if a vertical shaft is being 


OWN BOOK AND GUIDE. 


153 


sunk to take the course of ore at a certain depth, and the point 
of intersection will be apparent to his view. Lastly, we would 
recommend that the instruments for making 1 and keeping up a 
working plan should be a six or seven inch circular protractor, 
with double limb and vernier scale for reading off the angle, 
also a parallel ruler which travels on rollers as they are best 
both for expedition and accuracy. 

UNDERGROUND WORKS AND VENTILATION. 

As we have occupied a great deal more space in this work 
on the subject of surveying and the assaying of ores, &c., 
than we, at the commencement, intended to do, we shall 
endeavor to occupy as small a space as possible on the sub¬ 
ject of ventilation, but what we do say shall be practical 
and easy to understand, and the suggestions which we offer 
and advocate, as the means to obtain a safe, efficient and 
secure ventilation, shall be plain and with little expense in 
in their adoption, and simple and perfectly safe in their con¬ 
struction. 

The efficiency of any system of ventilation depends mainly 
upon an attention to three particulars : 1st, upon the opening of 
proper apertures for the admission of the atmospherical cur¬ 
rent; 2d, on some method of accelerating, and by this means 
renewing the voluinn of air in progress through the mines, 
and increase its velocity; 3d, in such a construction of the 
underground works that every part of the mine shall be ex¬ 
posed to the ventilating current. 

The least quantum of fresh air required in a fiery colliery 
is considered by some to be from 350 to 400 cubic feet per 
second, or the area of the passages multiplied by its velocity; 
but while we are strong advocates for large passages and a 
large quantity of air, we do contend that, as a general thing, 
that whenever an explosion happens at any colliery where 
these large quantities of air is said to be circulated through 
the mine, that the loss of life has always been the greatest, 
and if it was necessary, we could mention several instances 


154 


THE PRACTICAL MINERS’ 


that would bear us out in this assertion. We, however, do 
not wish or intend to be understood that we are contending 
that it is the large quantity of air that is the cause of it, but 
we do contend that it is either -the faulty way which it is 
applied, and the construction of the passages, and the drifts it 
travels through, or the quantity of air is not circulated as the 
managers say there is. The safety lamp is an excellent safe- 
guaid, and the memory of its inventor ought to be reverenced 
down to posterity, but we may with safety say to it, so far 
shalt thou go, and no further, and while we admire their con¬ 
struction and advocate their use and universal adoption, we 
do honestly believe that nine explosions out of every ten 
happen from the injudicious use of them, and that but few 
people are capable of using them. 

1 In order to illustrate how the atmos- 

A B pheric air will act when unassisted by 

“ ~~ artificial means, we suppose the annexed 

diagram, figure 1, to represent a tube 
c having each end bent upwards, at right- 

V ' ~ J angles with the horizontal portion, so as 

to form one level and two upright limbs, 
which we may suppose to be shafts, in this state the tube 
will be filled with air throughout, equally, the same as it 
might be filled with water, which would stand at the same 
height in each limb, and of course there would be no circu¬ 
lation. But if to the tube A we apply something to raise the 
temperature withinside, a new state of things instantly com¬ 
mences, and a current of fresh air will rush down the tube B, 
and passing along the horizontal part, C, will re-issue at A, 
thus ventilating on, as it were, sweeping the entire passage, 
and this operation will continue as long as the temperature 
remains the highest at A. 

There has been various methods brought into existence for 
ventilating mines besides the furnace ventilation, but nearly 
all the other devices have fallen to the ground and left the 
simple rarifying furnace, properly attended to, as the most 








OWN BOOK AND GUIDE. 


155 


efficacious application to the production of a well ventilated 
colliery; and we earnestly believe that although we read and 
hear of as much as 25,000 or 30,000 cubic feet of air passing 
through different mines per minute, that if a column of air six 
feet square is introduced and travels regularly through all parts 
of the mine, that an explosion would scarcely ever be heard of 
at the most dangerous mines, and the mines that such a quan¬ 
tity of air is regularly used in may be considered safe and 
healthy, providing the air is properly conveyed all over the 
works and the roads properly constructed that it travels 
through. A column of air 6 feet square=36 area, and sup¬ 
posing it to travel at the rate of 3 feet per second, viz: 
36 X 3=108 X 60=6.480 cubic feet per minute. The 
Americans who are the proprietors of collieries, especially 
those in Virginia, are more humane and charitable towards 
their perilous laborers than they are in England. Jt is true 
Lord Ashley compelled John Bull to adopt half measures to 
ameliorate the almost unbearable sufferings of the mining 
laborers, but which I believe are worse than none at all, and 
which have been proved to be entirely inadequate to remedy 
the evils that the poor English miners have to contend with, 
and they all remain to this day with all their concomitant 
horrors unmitigated. There are government inspectors em¬ 
ployed there, it is true, but they are selected and appointed 
by influence and not by their qualifications and competency 
to discharge the important duties incumbent on the offices 
they hold, as influence and affluence are constant companions 
there, and always go hand-in-hand in that country. The 
mortality among the mining population since the appointment 
of the inspectors of mines having increased, demonstrates 
their incompetency. In the year 1848 there was 466 men and 
boys killed in the mines of five counties, and in the following 
six months 332 men and boys were killed in-the same mines, 
which shows a melancholy increase, and in addition to this 
number killed there was in the same six months 132 men and 
boys severely injured from accidents. The majority of those 
that were killed were men of families, and had, by their 


THIS PRACTICAL MINERS’ 


156 


perilous exertions, contributed so much to the opulence of 
their employers and masters, yet their families, that were left 
unprovided for, were turned upon the world as itinerant 
beggars or compelled to go into the work-house, the regu¬ 
lations of which are known to be beyond endurance. But J 
rejoice to know that it is not the case in America, and that 
they do not satisfy themselves, as John Bull does, with a 
mere pretence to ameliorate the sufferings of the mining 
laborers, but that they do everything they can for their safety 
and comfort, regardless of expense, and if any of the laborers 
are killed, the survivors of them are allowed to live in the 
Company’s houses as long as they choose, and the proprietors 
of the colliery subscribe liberally to their comfort besides. 
This liberality on the part of the proprietors of Virginia 
collieries does not stop at the white man alone, but reaches 
the slaves; and I cannot, with justice to my feelings, quit this 
subject without relating some facts that my eyes have witnessed 
m Virginia. In England it is customary at the coal mines, 
and in the Sunday schools, to pray for the American slaves, 
and even the child, kneeling at its mother’s knee, is taught to 
pray for the slaves of America, but if they had seen as much 
ol the sufferings of the oppressed miners in England, and the 
happiness of the well-fed and contented American slaves, as the 
author of this work has done, their prayers would take a dif¬ 
ferent course. The slaves that work in the coal mines of Vir¬ 
ginia make more for pocket money for extra work than the ma¬ 
jority of English miners make to supporta large family and pay 
rent and taxes; and to show that the slaves’ wives are not for¬ 
gotten in the event of their husbands getting killed, I will re¬ 
late the gentlemanly and humane acts of Maj. VVoolridge, who 
was the President of the Midlothian Company, where an explo¬ 
sion took place in the year 1855, by which nine white men and 
boys were killed and thirty-six colored men. The President of 
the Company, with his accustomed benevolence and liberality 
gave arge sums of money to the white men’s wives, and to 
the slaves’ wives also, and bought the slaves’ wives mourning 
besides. A great many of the slaves fortunately happened to 


OWN BOOK AND GUIDE. 


157 

be out of the pit at the time the accident took place, and be¬ 
came alarmed and objected to go in the mines again, and as 
soon as it was made known to the president, he gave strict 
orders to the underground manager that no colored hand 
must be sent into the mines again except by their own consent. 

It is generally, and, I think, reasonably admitted, that the 
knowledge on ventilation in the north of England exceeds 
that of any other part of the world, and that knowledge is at 
this time gradually and necessarily improving in consequence 
of the deep shafts and extensive workings in the northern 
coal mines, and of their producing such considerable dis¬ 
charges of explosive gas. It may be well here to state ex¬ 
plicitly what principles ought to be adhered to, that come 
under the denomination of fiery mines. As a perfect knowledge 
of the disease is admitted to constitute half its remedy, I will 
endeavor briefly to explain my views in regard to the venti¬ 
lation of mines, and means that ought to be adopted in all 
fiery coal mines, not only to prevent accidents, but also for 
regaining the underground workings after an explosion has 
occurred, because it often happens that a greater number of 
lives are lost by the after-damp which results from explosions 
and from the want of air occasioned by the demolition of the 
doors and stoppings, than from the fire or the explosion it¬ 
self. The remedy and cure for these evils are within 
our reach and can be applied with little trouble and at a small 
expense. The main air roads should not only be made large 
enough, say at least six or eight feet square, but should be 
securely timbered so as to keep them from falling in and 
blocking it up, and thus retarding the progress of the venti¬ 
lating current. These roads ought to be examined by the 
manager or his gas-man at least twice every twenty-four 
hours, so that if a tumble takes place between their visits, they 
can have it removed immediately, to prevent friction and 
obstructions in the air. The ventilating* doors and stoppings 
are another important item in the safety of fiery mines, and I 
can safely say, without the slightest fear of contradiction, 
7* 


158 


THE PRACTICAL MINERS’ 


that the large and unexpected accumulations of gas in mines 
are the result of some derangement in the stoppings or doors. 
The stoppings are generally built of pine plank, not more 
than two inches thick, and as soon as the superincumbent 
weight comes on, they commence giving way, and a leakage 
immediately follows, thus depriving the futhermost part of 
the workings of pure air, and an explosion happens before 
the defective condition of the stoppings or doors is found out, 
and consequently killing all beyond it, either from the ex¬ 
plosion or from the after-damp, and 1 do contend and always 
shall, that temporary stoppings and defective ventilating doors, 
and the injudicious use of the safety lamp, give birth to all 
large colliery explosions, and I do contend that explosive gas 
is under the control of man, and that the Great Disposer of 
events has furnished mankind with ample means to control 
its destructive agency, if they will use them; but it so often, 
unfortunately, happens, in all parts of the world, that the 
golden image is valued more than human life. An explosion 
took place a few years ago at Clover Hill Mines, which the 
author of this work visited the second day after its occurrence, 
and by the request of the President of the Company and 
several of the surviving workmen, I went down the pits and 
assisted in restoring the ventilation of the mines and recover¬ 
ing the balance of the dead bodies that was then in the pit, 
which was two, as the others had been got out the, day 
previous to my going there. The mining agent in order to 
extricate himself from blame saddled the blame upon a colored 
man named Gilbert, for leaving a ventilating door open, but 
upon careful examination, I proved that the cause of the ex¬ 
plosion was not through Gilbert or the door but was from 
the defective state of the stoppings. Another explosion 
happened in the same year at the English Company’s Mines 
in Chesterfield county, Virginia, which the author of this 
work, by the desire of the manager, visited also. This ex¬ 
plosion was the result of the injudicious use of the safety 
lamp by one of the gas-men who was examining the workings 


OWN BOOK AND GUIDE. 


159 


early in the morning, and who had been up nearly all the 
night before drinking, and in all probability was drunk at the 
time he lighted the gas, not only killing himself, but those 
that were with him. Another explosion happened at the last 
named mines about two years after the one I have just named, 
and an examination by myself and others demonstrated 
beyond a doubt that the explosion was the result of a 
defective stopping and a temporary ventilating door, although 
the Midlothian Company have always done everything that 
was suggested to them for the health and safety of the under¬ 
ground laborers. The number of lives that was lost at the 
explosion that took place there in the year 1855 would not 
have been so great had there been stoppings and doors strong 
enough to resist the concussion of an explosion, as several 
of the men was not burned at all, and when we found them 
they lay placid in death and without a muscle of their faces 
being distorted. 

There ought to be at the bottom of every upcast shaft a 
furnace, of from forty-five to fifty feet area, placed within a 
good strong brick arch. The top of all upcast shafts ought 
to be protected from the influence of high winds, thus pro¬ 
viding an uninterrupted supply of a full and complete current 
of air. The doors in the gangways, instead of being made 
out of one-inch plank, as they now are, should be made out 
of good seasoned plank at least three inches thick and strong¬ 
ly and heavily ironed besides, and the posts or frames that 
the doors are hung in ought to be at least fifteen inches 
square, and a brick wall around them at least four feet thick, 
and well timbered on each side of the doors to take the 
weight that would otherwise fall on the door frame and cause 
it to twist and get out of its right form and prevent the door 
from shutting close, which produces leakage, and robs the 
interior of the workings of air. All the ventilating doors 
ought to be at least one hundred feet apart instead of being, 
as they generally are, only twenty or thirty feet apart. The 
stoppings that are built for the guidance of the air ought to 


160 


THE PRACTICAL MINERS’ 


be supported with the largest props that could be found, and 
set close together, and well cut into the floor and roof, and 
at least six feet of rock built against the planks of them all. 

1 hese arrangements may appear too expensive to some 
people, but to such, 1 beg leave to say, that the additional 
expense of these to the ordinary doors and stoppings would be 
but very trifling and is nothing when compared with the saving 
of life and property that may safely be calculated upon from 
their adoption and use, and with them and with sober, practi¬ 
cal, and careful gas-men, an explosion would scarcely ever be 
heard of, and the operations would go on uninterrupted. I don’t 
pretend to say that small accidents will not occur in the best 
regulated collieries, as they will happen from the non-compli¬ 
ance of the workmen with orders, but 1 will always say, that 
the large accidents can be avoided if the right steps are taken 
to avoid them. It often happens that after a colliery explo¬ 
sion has taken place, that the managers of the colliery boldly 
but unconsciously assert that the explosion was not from the 
ignition of inflammable gas, but that it was the result of some 
of the workmen lighting the blasting powder, or they will 
say that a small quantity of gas was lighted and came in con¬ 
tact with a lot of powder; but J will say, for the benefit and 
information of those who are unacquainted with mining 
operations, but who are otherwise more or less interested in 
the safety of its working, not to give credit to any such un¬ 
founded and erroneous statements, as three-fourths of them 
are entirely void of truth and are concocted and dictated by 
the meanest motives. It is true small quantities of powder is 
sometimes through carelessness lighted, but it is but very 
seldom, and even if it is so, this does not exonerate the gas¬ 
men from blame, as it is a part of their duty to see to that, 
equally as much as it is to see to the safe removal of the gas. 

It is reported from good authority, that knew the unsafe con¬ 
dition of the Sure Hope Pits at Clover Hill, where an ex¬ 
plosion took place in April, 1859, whereby nine men lost 
their lives, that at the time the explosion took place, there 


OWN BOOK AND GUIDE. 


161 


ivas a good deal of gas in another part of the workings that 
the explosion did not reach, or the loss of life and property 
would have been much greater than it was. The letter that 
was published in the Richmond Dispatch a few days after the 
explosion, which was said to be a letter from Mr. Marshall, 
was a got-up-thing to blind-fold public opinion, and any 
person that knows anything about the nature of mining 
operations, and possesses common sense, would have no 
trouble in discovering its meaning, and any person that is 
acquainted with the illiterate capacity of Mr. Marshall, will 
not hesitate one moment in saying that the letter was not 
dictated by him. One part of the letter states that the gas 
that was lighted occupied but a small space and could not 
have done much damage had it not been for the aid of blast¬ 
ing powder; another part of the letter states that large quan¬ 
tities of gas was released by cutting into a rich field of coal, 
but was cleaned out by the introduction of fresh air as fast as 
it made; another part of the letter acknowledges that there 
was gas in the pit and that a tumble in the air course caused 
it to flow back upon the workmen’s lights. The letter winds 
up by saying that the cause of the accident was quite clear to 
Mr. Marshall’s mind, and that it was a combination of circum¬ 
stances of rare coincidence that would scarcely ever happen 
again. T he sultriness of the weather, the day the explosion 
happened, and a few other things, was the cause of the acci¬ 
dent, which according to Mr. Marshall’s letter, are never to 
happen again; as much as to say that he or the author of the 
letter was the omnipotent God-head. 

Before we quit this subject we will beg leave to append 
another diagram, showing the bends or curves in the darts to 
represent the way the air travels or the way it would travel- 
if it was left to itself—it also shows the difference of its 
specific gravity to that of inflammable gas. This subject has 
caused the author of this work to experience many a sleepless 
night, and he has often wondered how it was that science, 
with its accumulated ingenuity, had not found out something 


162 


THE PRACTICAL MINERS’ 


to neutralize explosive gas; but although science has ac¬ 
complished much beyond our gone-by anticipations, this 
achievement has hitherto baffled the wisdom of all science 
and skill. 

In laying off shafts for a colliery, the upcast shaft should 
always be the shallowest by at least sixty or seventy feet, 
and if it can be arranged one hundred feet shallower it would 
be still better and would render the underground workings 
much safer as regards ventilation, as there would always be 
a continual rush of fresh air into the down-cast shaft, and 
there would require but very little artificial means to be applied 
to secure an efficient and safe ventilation. Diagram No. 2 
will illustrate our meaning on this subject, and whenever the 
location of the coal to be got will not justify such an arrange¬ 
ment in the shafts as we have just suggested, there should 
by all means be an additional height added at the top of the 
upcast shaft, and should be made as strong as possible with 
good seasoned timber, and perfectly air-tight. 




ou9 ?j Bt ts i st ^n 







*iaaj 009 IPOS }stotiA\o<2 


See page 162. S. Stands for Stoppings. 

P. Stands for Pillars. 
































































































It will be seen by the above diagram that the accumulation of gas would be much greater than it is, were it 
not for the doors that force the air into the two places where the coal has been excavated. 


OWN BOOK AND GUIDE 


163 


400 FEET DEEP 



500 FEET DEEP 


































164 


the practical miners’ 


REMARKS 

Upon the middle division of Eastern Virginia Coal Field , 
with some remarks upon the use and value of coal and iron. 

The Eastern Virginia coal field extends over a portion of six 
counties, viz: Chesterfield, Powhatan, Henrico, Amelia, Gooch¬ 
land and Hanover. The James river is supposed to be about 
the centre of it and the Appomattox traverses its southern 
boundary. The level course of this coal field is about N. N. 
E. 29° and S. S. W. 29°. The remarks that I shall offer upon this 
coal field shall be those of a practical miner gained by twelve 
years expeiience in working and seeing the various coal ope¬ 
rations in this district, and also from close and careful exami¬ 
nations of the outcrops and the strata through the greatest 
portions of it. Although this coal field embraces an area of 
upwards of 100 square miles it may safely be said that it is at 
the present time almost untouched. The coal from this dis¬ 
trict can be brought to tide-water in about one hour’s travel 
by railway and boat transit. The quality of this coal for all 
manufacturing purposes, and for making gas, and for fuel for 
steam vessels cannot be surpassed by any coal in the world, 
and when we consider its superficial extent, its proximity to 
tide-water, and its superior quality, we are filled with astonish¬ 
ment to know that men of capital do not invest their money 
and develop these immeasurable deposits of mineral treasures 
that are incomputable in value. The following letter will 
satisfy anybody as to the quality of the Virginia coal, especial¬ 
ly when they know the high and authentic source that the 
letter emanated from. The letter reads thus :_ 

U. S. Revenue Steamer Legure, ) 
Washington, April 23 d, 1847. \ 

Having been requested when in Richmond, Virginia, to make a re- 
port of the quality of the Virginia coal received from there on board 
this vessel, I cheerfully comply, and have no hesitation in saying that 
it is the best quality of bituminous coal that I have ever used. It 
burns freely, makes steam very fast, is easy to fire with, leaves no 
clinker, but few ashes, and its consumption compared with other bi- 


OWN BOOK AND GUIDE. 


1G5 

tuminous coal that I have used, is much smaller, and I have no hesi¬ 
tation in recommending it in the highest terms as an article for use in 
steam vessels. You are at liberty to use this letter in .any way that 
you may deem best to advance the reputation of the Virginia coal. 

Very respectfully, 

JOHN DOUGHERTY, 

Chief Engineer U. S. Revenue Marine. 

Coal mining operations have been carried on more or less 
in Chesterfield county for a period of sixty years. In the year 
1835, the Midlothian company obtained a charter from the 
General Assembly of Virginia, to work coal upon the tracts 
called the grove and midlothian, which was then supposed to 
contain large bodies of coal, the two comprising 400| acres. 
Capital $100,000. The charter to continue in force twenty 
years. In 1836, an amended one was got and the capital in¬ 
creased to $300,000. They commenced raising coal in 1840 
and continued doing an active business up to 1855, since 
which time this company have met with some serious and 
heavy losses by accidents, but the President of the company 
with undaunted courage and perseverance has enlarged the 
operations, and with care and good management the company 
will soon be able to do a much larger business than they ever 
have done as they have purchased Riley’s Hill, and leased a 
portion of the English company’s property, in both of which 
properties there is a large quantity of coal, all of which is to 
the rise of the midlothian works and can be raised with very 
little expense. This company is sinking a large shaft to the 
west of their present workings, which will develop a large 
quantity of unexplored land to the north, to the south, and to 
the west, but it will be sometime before the coal is reached, as 
it may be from 900 to 1100 feet deep to the coal. The thick 
coal of Chesterfield county ought not to be got in the way it 
has been. The system answers very well in some parts of 
England, but there are local circumstances to be considered. 
The irregularities that are so frequently met with in working 
this coal would be an advantage to the operations in the thick 


166 


THE PRACTICAL MINERS’ 


coal seams in England, while they are a disadvantage in work¬ 
ing.it here. There the coal and metals are almost flat in some 
places, but here the coal and metals have a very heavy pitch. 
In opening out new mines here, great care should be taken to 
leave sufficient ribs of coal, with as few holeings as possible, 
and the work should be laid off in sections until the further¬ 
most extent of the operations are reached, during which time 
every preparation ought to be made for dams at each section, 
and a good return air course opened and well secured to the 
rise, that let whatever contingency may happen in the shape 
of spontaneous fire or otherwise, that all would be ready to be 
made secure in a few hours at any time and the operations 
would go on uninterrupted, which is a great desideratum in 
this State; and in my opinion more coal could be obtained by 
working on this plan than by the old mode of working which 
has hitherto been adopted. There are very extensive properties 
within thirteen miles of Richmond, and which are quite conve¬ 
nient to the railroad that contains almost inexhaustable depo¬ 
sits of coal. Among them I will mention Mr. P. T. Johnson’s 
property, which embraces an area of 1500 acres, a great por¬ 
tion of which is supposed to contain coal of a superior quality, 
and surface indications bear us out in saying that a good 
workable seam of coal could be found on this property at a 
moderate depth. There is Mr. Thomas Burfoot’s property 
which lies on the side of James river, a few miles above Rich¬ 
mond, which embraces an area of 400 acres, nearly all of 
which contain coal, coke, and iron ore. There are several 
other properties belonging to private individuals in Chesterfield 
county, that contain large bodies of coal, but the present state 
of the coal trade will not justify a sufficient outlay to put these 
properties in operation. If the iron and coal trade in America 
could have its legitimate protection that belongs to it, the coal 
mines and iron foundries would be increased ten fold, and 
where there is one man now employed in those branches of 
business, there would be hundreds employed then, and the 
money that would be circulated in every species of business 


OWN BOOK AND GUIDE. 


167 

would be incalculable. Let us look at the number of hands 
that are employed in the coal mines of England and Scotland, 
say nothing of the vast numbers that are employed there in 
nufacturing of iron, a great deal of which is imported 
to this country, as well as coal, and the money sent awav to 
pay for it that ought to be kept here and circulated among 
trade at home. The coal that is annually used in the metro¬ 
polis of England alone is 600,000 tons for manufacturing and 
domestic purposes, and the coasting vessels take away annual¬ 
ly about 9,360,000 tons, which employs 120,000 persons un¬ 
derground, besides those that are employed on the surface. 
Scotland employs 22,250 men and boys underground and 
raises annually 7,250,000 tons, which is equal to 340 tons for 
each underground hand yearly. The produce from the whole 
of the English mines is about 37,000,000 tons annually, one- 
fourth of which is sent to places that ought to be supplied from 
the mines of America. It is as unreasonable and equally as un¬ 
necessary to buy water from other countries to put into the 
mighty Atlantic, as it is to import coal and iron into the United 
States, where they both are so plentiful and cannot be exhausted 
for thousands of generations to come. The time has arrived 
when the quantity of coal annually consumed by any nation 
may be taken as an exponent of its power. Its commercial 
greatness, ocean and inland, and it may safely be said that com¬ 
merce is the President of nations, and coal is Secretary of 
State. The progress of civilization may in any country be 
measured by the greater or less use of coal and iron ; the time 
has been when cutting, digging and hewing was all done by 
sharpened stones, and the progress in the working of metals 
is illustrated by articles of different kinds being found in the 
ancient burying grounds. The stone period came first for 
cutting, hewing and digging as we have evidence of this de¬ 
posited in different museums throughout the world. Next to 
the stone period came the copper period, and then came iron, 
and it is inconceivable to what different purposes iron can be 
applied where no other materials or all other materials com- 


168 


THE PRACTICAL MINERS’ 


bined could not answer the purposes. The cambric needle 
and the nasmyth hammer cannot be made without iron. The 
two hundred pound ball peacemaker, and the rifles and swords 
that helped so much to gain the independence of this great 
Republic, could not have been made without iron and coal. 
Tim surgeon’s instruments, or the anchor to a ship, or Rod¬ 
gers’ razors, or the steam engine, or the agricultural imple¬ 
ments, and a thousand other things that contribute so largely 
to our comforts, could none of them be made without iron 
and coal. Jn the preface of this work we took the liberty to 
urge Americans to learn their sons the art of mining, and said 
everything we could to show the necessity of learning the 
practical part of mining, by going through the different rudi¬ 
ments m the mines and of learning the theoretical part in 
schools and colleges. The former would qualify them for 
the ordinary management of a colliery, and would‘teach them 
how to set work by contract, &c., and the latter would qual¬ 
ify them to understand the different gases both practically and 
chemically and to manage them in an efficient and masterly 
manner. We said in the preface of this work, that if a mining 
profession was a dangerous one it was not a degrading one, 
and that the thought of the incalculable good that mankind de¬ 
rives from the innumerable uses of coal, ought of itself to in¬ 
duce some of the Americans to learn the art of mining, instead 
of over-crowding the unhealthy profession of medicine and 
law. As a proof that a mining occupation is not a degrading 
one, we will mention that the'celebrated Dr. Hutton, was 
originally a coal digger and was employed in Long Benton 
Colliery. Mr. Stephenson, the intelligent engineer of the Li¬ 
verpool and Manchester railway, was a coal miner. The Rev. 
W. Huntington, an eccentric but talented preacher in the city 
of London, was a collier. Mr. Thomas Bewick, the celebrat¬ 
ed xylographer and illustrator of nature, may be mentioned as 
another instance whose father was a collier at Hexham Colli¬ 
ery, and Thomas with his other brothers was at a early ao- e 
immured into the subterranean cavern of darkness, to earn his 


169 


OWN BOOK AND GUIDE. 

bread by the sweat of his brow and lie has been heard to say 
hat the remotest recollections of his powerful and tenacious 
memory was that of lying for hours together on his side un¬ 
dermining coal by the glimmering of a candle, plying the pick 
as hard as he could with his hands. Those hands were after¬ 
wards destined to elevate the arts, illustrate nature and promul¬ 
gate her truths to the delight and the instruction of the moral 
and intellectual world, and we have known some of the most ta¬ 
lented preachers that ever adorned the sacred desk to come 
from colliers, and was brought up in the mines from their in¬ 
fancy. It may not be and is not a proof of the general intel¬ 
ligence of any body of operatives that men of talent have oc¬ 
casionally risen from among them to distinguished stations in 
society, but it is natural to associate the ultimate fame of any 
individual with his original calling. 


SEARCHING FOR COAL. 

The most usual method of ascertaining the mineral con¬ 
tents of any given piece of unexplored land is by boring.— 
This process often proves unsatisfactory, but with an experi¬ 
enced collier at its head, who thoroughly understands the way 
of testing the different metals or substances that the boring 
makes, boring may be performed to an advantage, and with 
but little expense and the thickness of the minerals sought for 
can be ascertained, and the actual depth to it, so that the owner 
of the land can determine whether its quality and thickness 
will justify the sinking of a shaft, and the erection of machine¬ 
ry or not. The following sketch is a representation of the 
apparatus which is generally used for boring and the way it 
ought to be constructed, and we have appended the following 
diagram for the information of those who are unacquainted 
with it or its mode of operation or construction. 


170 


THE PRACTICAL MINERS’ 



A spot being fixed upon, the first object of the workmen 
after digging out a hole some 8 or 10 feet deep, is to obtain a 
stout springing pole A, which should be 12 or 14 yards long 
and which should be selected from a fresh felled tree. It 
should be securely fastened down at the thick end and a short 
distance from which it rests upon its bearer B, near the small 
end a wooden stave is passed through affording sufficient hand 
hold for two men who will stand on the platform C, over this 
platform and exactly over the spot where the boring is to take 
place, a triangle D, is erected consisting of three poles fasten¬ 
ed at the apex and sustaining a pully block and rope, the lat¬ 
ter attached to the windlass E, a flooring of planks F, G, is 
then laid down having a hole in the centre through which the 
rods are to work 5 these rods II, K, are of iron, 4 or 5 feet 
long, 1 inch in diameter, which should be tapped with good 
screws at their ends } the lowermost rod which operates upon 
the metals is a chisel K, the uppermost terminates in a stout 
ring through which passes the lower cross-piece, and which in 
working is taken hold of by two men, it is also suspended to 
the springing pole by a chain. One of the rods is formed at 
the end with a shell like an augur which is used at intervals to 
bring up the productions of the bore hole. The mode of 
operations are as follows: The rods are pushed through the hole 
in the planks, the two men on the platform take hold of the cross 
stave at the end of the springing pole and work it up and down, 
while the man below having hold of the cross-piece work 















OWN BOOK AND GUIDE. 


171 


steadily round the hole. The diameter of the boring rods can 
be regulated to suit the operators. M, is the spanner used in 
screwing and unscrewing the rods, and N, is an iron fork, the 
prongs of which are placed across the rods below the swell 
and in contact with the floor to prevent the lower rods from 
falling while the upper ones are being screwed off or on. By 
this method and with great care, an examination of the strata 
and the thickness of the coal or mineral sought for is made at 
a small expense, but the best way in my opinion is to first find 
the basis upon which the coal rests, and if the indications for 
coal or the mineral are good, ascertain the way the metals dip 
and go some 60 or 70 feet on the surface to the dip, and sink 
down till you find the same seam that you have seen on the 
surface, and if it has increased enough in thickness in that 
distance to justify the sinking of a shaft further to the dip and 
erect machinery, it is better than boring. Or a slope can 
be driven down with the seam from the surface which will 
prove it equally as well. Of all the experiments that a man 
of sensibility can be employed in, there is perhaps none more 
amusing or more engaging or more delightful than a success¬ 
ful trial upon the vestige, or appearances of a good seam of 
coal, or the discovery of good minerals of any kind. When 
you are attending the men who are digging either downward 
or forward upon the vestige of the seam, and the indications 
are increasing and still growing better under your eye, the 
spirit of curiosity and attention is awakened and all the powers 
of expectation are elevated in pleasing hopes of success, and 
when your wishes are at length actually crowned with suc¬ 
cess, when you have discovered a good seam of coal of suffi¬ 
cient thickness and that all circumstances are favorable, the 
heart then triumphs in the accomplishment of its wishes with 
solid and satisfactory joy. And 1 believe there is more ration¬ 
al delight, more substantial pleasure and happiness to be en¬ 
joyed in such scenes as this than in all the amusements which 
luxury ever did invent or ever can. But oh, the mortification 
attendant upon disappointment in these experiments are beyond 
expression. 


172 THE PRACTICAL MINERS’ OWN BOOK, &C. 

Although I have in several places in this work, advocated 
to the best of my ability, protection to American manufacto¬ 
ries and the coal trade, I cannot close this work without say¬ 
ing that if these branches of business are as much neglected in 
the future as they now are by Government, they will become 
entirely paralysed, and manufactories of every description in 
this great country will sink into comparative insignificance, 
and this country will lose its greatness, superiority and envied 
pre-eminence it possesses or ought to possess over all other 
nations in the whole world. 

Capitalists who have invested their money in these branch¬ 
es of enterprise, may as well try to breathe in vacuity as ex¬ 
pect to be successful as long as they are deprived of that legit¬ 
imate protection which is due them, and the nature of the bus¬ 
iness they embark in so reasonably demands. 

It is to be hoped that at the approaching presidential elec¬ 
tion, that mechanics and laborers of every class who form the 
bone and sinew of this country, will look to their interest and 
that of their country, and remember that they are not in a 
country that is governed by kings or queens, or by emperors, 
but that they have the inexpressible pleasure of knowing they 
are citizens of a country, where the President and Congress¬ 
men are their servants, instead of their kings or queens, and 
which constitution gives them the prerogative to discharge 
them if they are not faithful. 



















































































































































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